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by Chris Woodford . Last updated: July 23, 2023.

Photo: Sound is energy we hear made by things that vibrate. Photo by William R. Goodwin courtesy of US Navy and Wikimedia Commons .

What is sound?

Photo: Sensing with sound: Light doesn't travel well through ocean water: over half the light falling on the sea surface is absorbed within the first meter of water; 100m down and only 1 percent of the surface light remains. That's largely why mighty creatures of the deep rely on sound for communication and navigation. Whales, famously, "talk" to one another across entire ocean basins, while dolphins use sound, like bats, for echolocation. Photo by Bill Thompson courtesy of US Fish and Wildlife Service .

Robert Boyle's classic experiment

Artwork: Robert Boyle's famous experiment with an alarm clock.

How sound travels

Artwork: Sound waves and ocean waves compared. Top: Sound waves are longitudinal waves: the air moves back and forth along the same line as the wave travels, making alternate patterns of compressions and rarefactions. Bottom: Ocean waves are transverse waves: the water moves back and forth at right angles to the line in which the wave travels.

The science of sound waves

Picture: Reflected sound is extremely useful for "seeing" underwater where light doesn't really travel—that's the basic idea behind sonar. Here's a side-scan sonar (reflected sound) image of a World War II boat wrecked on the seabed. Photo courtesy of U.S. National Oceanographic and Atmospheric Administration, US Navy, and Wikimedia Commons .

Whispering galleries and amphitheaters

Photos by Carol M. Highsmith: 1) The Capitol in Washington, DC has a whispering gallery inside its dome. Photo credit: The George F. Landegger Collection of District of Columbia Photographs in Carol M. Highsmith's America, Library of Congress , Prints and Photographs Division. 2) It's easy to hear people talking in the curved memorial amphitheater building at Arlington National Cemetery, Arlington, Virginia. Photo credit: Photographs in the Carol M. Highsmith Archive, Library of Congress , Prints and Photographs Division.

Measuring waves

Understanding amplitude and frequency, why instruments sound different, the speed of sound.

Photo: Breaking through the sound barrier creates a sonic boom. The mist you can see, which is called a condensation cloud, isn't necessarily caused by an aircraft flying supersonic: it can occur at lower speeds too. It happens because moist air condenses due to the shock waves created by the plane. You might expect the plane to compress the air as it slices through. But the shock waves it generates alternately expand and contract the air, producing both compressions and rarefactions. The rarefactions cause very low pressure and it's these that make moisture in the air condense, producing the cloud you see here. Photo by John Gay courtesy of US Navy and Wikimedia Commons .

Why does sound go faster in some things than in others?

Chart: Generally, sound travels faster in solids (right) than in liquids (middle) or gases (left)... but there are exceptions!

How to measure the speed of sound

Sound in practice, if you liked this article..., find out more, on this website.

• Electric guitars
• Speech synthesis
• Synthesizers

On other sites

• Explore Sound : A comprehensive educational site from the Acoustical Society of America, with activities for students of all ages.
• Sound Waves : A great collection of interactive science lessons from the University of Salford, which explains what sound waves are and the different ways in which they behave.

Educational books for younger readers

• Sound (Science in a Flash) by Georgia Amson-Bradshaw. Franklin Watts/Hachette, 2020. Simple facts, experiments, and quizzes fill this book; the visually exciting design will appeal to reluctant readers. Also for ages 7–9.
• Sound by Angela Royston. Raintree, 2017. A basic introduction to sound and musical sounds, including simple activities. Ages 7–9.
• Experimenting with Sound Science Projects by Robert Gardner. Enslow Publishers, 2013. A comprehensive 120-page introduction, running through the science of sound in some detail, with plenty of hands-on projects and activities (including welcome coverage of how to run controlled experiments using the scientific method). Ages 9–12.
• Cool Science: Experiments with Sound and Hearing by Chris Woodford. Gareth Stevens Inc, 2010. One of my own books, this is a short introduction to sound through practical activities, for ages 9–12.
• Adventures in Sound with Max Axiom, Super Scientist by Emily Sohn. Capstone, 2007. The original, graphic novel (comic book) format should appeal to reluctant readers. Ages 8–10.

Popular science

• The Sound Book: The Science of the Sonic Wonders of the World by Trevor Cox. W. W. Norton, 2014. An entertaining tour through everyday sound science.

Academic books

• Master Handbook of Acoustics by F. Alton Everest and Ken Pohlmann. McGraw-Hill Education, 2015. A comprehensive reference for undergraduates and sound-design professionals.
• The Science of Sound by Thomas D. Rossing, Paul A. Wheeler, and F. Richard Moore. Pearson, 2013. One of the most popular general undergraduate texts.

Text copyright © Chris Woodford 2009, 2021. All rights reserved. Full copyright notice and terms of use .

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Key Questions

Scientifically, this is a very difficult question to answer. The reason is simply that the word "best" is difficult to interpret. In science, understanding the question is often as important as the answer.

You might be asking about the speed of sound. You might be asking about energy loss of sound (e.g. sound traveling through cotton).

Then again, you might be asking about materials which transmit a range of frequencies with very little dispersion (difference between the wave speeds for various pitches). You might look up soliton waves in narrow channels for an example of a wave that stays together over a long distance.

And yet again, you might be asking about materials which can pickup sound from air; an impedance match.

What materials have the highest speed of sound? This is the easiest question to answer, so we'll start with that. In general, the speed of sound in a material varies with the stiffness and mass of that material. Sound traveling through hardened steel will cary much faster than traveling through air. Many materials are characterized by something called a Young's Modulus. You should find that the speed of sound increases with higher Young's Modulus. A search for materials with a high speed of sound or a high Young's Modulus should turn up interesting answers.

One of the most dense materials known is the neutron star. One drop-sized piece of a neutron star has the same mass greater than the giant pyramid at Giza (about a billion tons). Some people calculate the speed of sound in a neutron star to be very close to the speed of light.

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Sound as a Longitudinal Wave

• Sound is a Mechanical Wave
• Sound is a Longitudinal Wave
• Sound is a Pressure Wave

Sound waves in air (and any fluid medium) are longitudinal waves because particles of the medium through which the sound is transported vibrate parallel to the direction that the sound wave moves. A vibrating string can create longitudinal waves as depicted in the animation below. As the vibrating string moves in the forward direction, it begins to push upon surrounding air molecules, moving them to the right towards their nearest neighbor. This causes the air molecules to the right of the string to be compressed into a small region of space. As the vibrating string moves in the reverse direction (leftward), it lowers the pressure of the air immediately to its right, thus causing air molecules to move back leftward. The lower pressure to the right of the string causes air molecules in that region immediately to the right of the string to expand into a large region of space. The back and forth vibration of the string causes individual air molecules (or a layer of air molecules) in the region immediately to the right of the string to continually vibrate back and forth horizontally. The molecules move rightward as the string moves rightward and then leftward as the string moves leftward. These back and forth vibrations are imparted to adjacent neighbors by particle-to-particle interaction. Other surrounding particles begin to move rightward and leftward, thus sending a wave to the right. Since air molecules (the particles of the medium) are moving in a direction that is parallel to the direction that the wave moves, the sound wave is referred to as a longitudinal wave. The result of such longitudinal vibrations is the creation of compressions and rarefactions within the air.

Regardless of the source of the sound wave - whether it is a vibrating string or the vibrating tines of a tuning fork - sound waves traveling through air are longitudinal waves. And the essential characteristic of a longitudinal wave that distinguishes it from other types of waves is that the particles of the medium move in a direction parallel to the direction of energy transport.

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17.3: Speed of Sound

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Learning Objectives

• Explain the relationship between wavelength and frequency of sound
• Determine the speed of sound in different media
• Derive the equation for the speed of sound in air
• Determine the speed of sound in air for a given temperature

Sound, like all waves, travels at a certain speed and has the properties of frequency and wavelength. You can observe direct evidence of the speed of sound while watching a fireworks display (Figure \(\PageIndex{1}\)). You see the flash of an explosion well before you hear its sound and possibly feel the pressure wave, implying both that sound travels at a finite speed and that it is much slower than light.

The difference between the speed of light and the speed of sound can also be experienced during an electrical storm. The flash of lighting is often seen before the clap of thunder. You may have heard that if you count the number of seconds between the flash and the sound, you can estimate the distance to the source. Every five seconds converts to about one mile. The velocity of any wave is related to its frequency and wavelength by

\[v = f \lambda, \label{17.3}\]

where \(v\) is the speed of the wave, \(f\) is its frequency, and \(\lambda\) is its wavelength. Recall from Waves that the wavelength is the length of the wave as measured between sequential identical points. For example, for a surface water wave or sinusoidal wave on a string, the wavelength can be measured between any two convenient sequential points with the same height and slope, such as between two sequential crests or two sequential troughs. Similarly, the wavelength of a sound wave is the distance between sequential identical parts of a wave—for example, between sequential compressions (Figure \(\PageIndex{2}\)). The frequency is the same as that of the source and is the number of waves that pass a point per unit time.

Speed of Sound in Various Media

Table \(\PageIndex{1}\) shows that the speed of sound varies greatly in different media. The speed of sound in a medium depends on how quickly vibrational energy can be transferred through the medium. For this reason, the derivation of the speed of sound in a medium depends on the medium and on the state of the medium. In general, the equation for the speed of a mechanical wave in a medium depends on the square root of the restoring force, or the elastic property, divided by the inertial property,

\[v = \sqrt{\frac{\text{elastic property}}{\text{inertial property}}} \ldotp\]

Also, sound waves satisfy the wave equation derived in Waves ,

\[\frac{\partial^{2} y (x,t)}{\partial x^{2}} = \frac{1}{v^{2}} \frac{\partial^{2} y (x,t)}{\partial t^{2}} \ldotp\]

Recall from Waves that the speed of a wave on a string is equal to \(v = \sqrt{\frac{F_{T}}{\mu}}\), where the restoring force is the tension in the string F T and the linear density \(\mu\) is the inertial property. In a fluid, the speed of sound depends on the bulk modulus and the density,

\[v = \sqrt{\frac{B}{\rho}} \ldotp \label{17.4}\]

The speed of sound in a solid the depends on the Young’s modulus of the medium and the density,

\[v = \sqrt{\frac{Y}{\rho}} \ldotp \label{17.5}\]

In an ideal gas (see The Kinetic Theory of Gases ), the equation for the speed of sound is

\[v = \sqrt{\frac{\gamma RT_{K}}{M}}, \label{17.6}\]

where \(\gamma\) is the adiabatic index, R = 8.31 J/mol • K is the gas constant, T K is the absolute temperature in kelvins, and M is the molecular mass. In general, the more rigid (or less compressible) the medium, the faster the speed of sound. This observation is analogous to the fact that the frequency of simple harmonic motion is directly proportional to the stiffness of the oscillating object as measured by k, the spring constant. The greater the density of a medium, the slower the speed of sound. This observation is analogous to the fact that the frequency of a simple harmonic motion is inversely proportional to m, the mass of the oscillating object. The speed of sound in air is low, because air is easily compressible. Because liquids and solids are relatively rigid and very difficult to compress, the speed of sound in such media is generally greater than in gases.

Because the speed of sound depends on the density of the material, and the density depends on the temperature, there is a relationship between the temperature in a given medium and the speed of sound in the medium. For air at sea level, the speed of sound is given by

\[v = 331\; m/s \sqrt{1 + \frac{T_{C}}{273 °C}} = 331\; m/s \sqrt{\frac{T_{K}}{273\; K}} \label{17.7}\]

where the temperature in the first equation (denoted as T C ) is in degrees Celsius and the temperature in the second equation (denoted as T K ) is in kelvins. The speed of sound in gases is related to the average speed of particles in the gas,

\[v_{rms} = \sqrt{\frac{3k_{B}T}{m}}.\]

where \(k_B\) is the Boltzmann constant (1.38 x 10 −23 J/K) and m is the mass of each (identical) particle in the gas. Note that v refers to the speed of the coherent propagation of a disturbance (the wave), whereas \(v_{rms}\) describes the speeds of particles in random directions. Thus, it is reasonable that the speed of sound in air and other gases should depend on the square root of temperature. While not negligible, this is not a strong dependence. At 0°C , the speed of sound is 331 m/s, whereas at 20.0 °C, it is 343 m/s, less than a 4% increase. Figure \(\PageIndex{3}\) shows how a bat uses the speed of sound to sense distances.

Derivation of the Speed of Sound in Air

As stated earlier, the speed of sound in a medium depends on the medium and the state of the medium. The derivation of the equation for the speed of sound in air starts with the mass flow rate and continuity equation discussed in Fluid Mechanics . Consider fluid flow through a pipe with cross-sectional area \(A\) (Figure \(\PageIndex{4}\)). The mass in a small volume of length \(x\) of the pipe is equal to the density times the volume, or

\[m = \rho V = \rho Ax.\]

The mass flow rate is

\[\frac{dm}{dt} = \frac{d}{dt} (\rho V) = \frac{d}{dt} (\rho Ax) = \rho A \frac{dx}{dt} = \rho Av \ldotp\]

The continuity equation from Fluid Mechanics states that the mass flow rate into a volume has to equal the mass flow rate out of the volume,

\[\rho_{in} A_{in}v_{in} = \rho_{out} A_{out}v_{out}.\]

Now consider a sound wave moving through a parcel of air. A parcel of air is a small volume of air with imaginary boundaries (Figure \(\PageIndex{5}\)). The density, temperature, and velocity on one side of the volume of the fluid are given as \(\rho\), T, v, and on the other side are \(\rho\) + d\(\rho\), \(T + dT\), \(v + dv\).

The continuity equation states that the mass flow rate entering the volume is equal to the mass flow rate leaving the volume, so

\[\rho Av = (\rho + d \rho)A(v + dv) \ldotp\]

This equation can be simplified, noting that the area cancels and considering that the multiplication of two infinitesimals is approximately equal to zero: d\(\rho\)(dv) ≈ 0,

\[\begin{split} \rho v & = (\rho + d \rho)(v + dv) \\ & = \rho v + \rho (dv) + (d \rho)v + (d \rho)(dv) \\ 0 & = \rho (dv) + (d \rho) v \\ \rho\; dv & = -v\; d \rho \ldotp \end{split}\]

The net force on the volume of fluid (Figure \(\PageIndex{6}\)) equals the sum of the forces on the left face and the right face:

\[\begin{split} F_{net} & = p\; dy\; dz - (p + dp)\; dy\; dz \ & = p\; dy\; dz\; - p\; dy\; dz - dp\; dy\; dz \\ & = -dp\; dy\; dz \\ ma & = -dp\; dy\; dz \ldotp \end{split}\]

Figure \(\PageIndex{6}\):

The acceleration is the force divided by the mass and the mass is equal to the density times the volume, m = \(\rho\)V = \(\rho\) dx dy dz. We have

\[\begin{split} ma & = -dp\; dy\; dz \\ a & = - \frac{dp\; dy\; dz}{m} = - \frac{dp\; dy\; dz}{\rho\; dx\; dy\; dz} = - \frac{dp}{\rho\; dx} \\ \frac{dv}{dt} & = - \frac{dp}{\rho\; dx} \\ dv & = - \frac{dp}{\rho dx} dt = - \frac{dp}{\rho} \frac{1}{v} \\ \rho v\; dv & = -dp \ldotp \end{split}\]

From the continuity equation \(\rho\) dv = −vd\(\rho\), we obtain

\[\begin{split} \rho v\; dv & = -dp \\ (-v\; d \rho)v & = -dp \\ v & = \sqrt{\frac{dp}{d \rho}} \ldotp \end{split}\]

Consider a sound wave moving through air. During the process of compression and expansion of the gas, no heat is added or removed from the system. A process where heat is not added or removed from the system is known as an adiabatic system. Adiabatic processes are covered in detail in The First Law of Thermodynamics , but for now it is sufficient to say that for an adiabatic process, \(pV^{\gamma} = \text{constant}\), where \(p\) is the pressure, \(V\) is the volume, and gamma (\(\gamma\)) is a constant that depends on the gas. For air, \(\gamma\) = 1.40. The density equals the number of moles times the molar mass divided by the volume, so the volume is equal to V = \(\frac{nM}{\rho}\). The number of moles and the molar mass are constant and can be absorbed into the constant p \(\left(\dfrac{1}{\rho}\right)^{\gamma}\) = constant. Taking the natural logarithm of both sides yields ln p − \(\gamma\) ln \(\rho\) = constant. Differentiating with respect to the density, the equation becomes

\[\begin{split} \ln p - \gamma \ln \rho & = constant \\ \frac{d}{d \rho} (\ln p - \gamma \ln \rho) & = \frac{d}{d \rho} (constant) \\ \frac{1}{p} \frac{dp}{d \rho} - \frac{\gamma}{\rho} & = 0 \\ \frac{dp}{d \rho} & = \frac{\gamma p}{\rho} \ldotp \end{split}\]

If the air can be considered an ideal gas, we can use the ideal gas law:

\[\begin{split} pV & = nRT = \frac{m}{M} RT \\ p & = \frac{m}{V} \frac{RT}{M} = \rho \frac{RT}{M} \ldotp \end{split}\]

Here M is the molar mass of air:

\[\frac{dp}{d \rho} = \frac{\gamma p}{\rho} = \frac{\gamma \left(\rho \frac{RT}{M}\right)}{\rho} = \frac{\gamma RT}{M} \ldotp\]

Since the speed of sound is equal to v = \(\sqrt{\frac{dp}{d \rho}}\), the speed is equal to

\[v = \sqrt{\frac{\gamma RT}{M}} \ldotp\]

Note that the velocity is faster at higher temperatures and slower for heavier gases. For air, \(\gamma\) = 1.4, M = 0.02897 kg/mol, and R = 8.31 J/mol • K. If the temperature is T C = 20 °C (T = 293 K), the speed of sound is v = 343 m/s. The equation for the speed of sound in air v = \(\sqrt{\frac{\gamma RT}{M}}\) can be simplified to give the equation for the speed of sound in air as a function of absolute temperature:

\[\begin{split} v & = \sqrt{\frac{\gamma RT}{M}} \\ & = \sqrt{\frac{\gamma RT}{M} \left(\dfrac{273\; K}{273\; K}\right)} = \sqrt{\frac{(273\; K) \gamma R}{M}} \sqrt{\frac{T}{273\; K}} \\ & \approx 331\; m/s \sqrt{\frac{T}{273\; K}} \ldotp \end{split}\]

One of the more important properties of sound is that its speed is nearly independent of the frequency. This independence is certainly true in open air for sounds in the audible range. If this independence were not true, you would certainly notice it for music played by a marching band in a football stadium, for example. Suppose that high-frequency sounds traveled faster—then the farther you were from the band, the more the sound from the low-pitch instruments would lag that from the high-pitch ones. But the music from all instruments arrives in cadence independent of distance, so all frequencies must travel at nearly the same speed. Recall that

\[v = f \lambda \ldotp\]

In a given medium under fixed conditions, \(v\) is constant, so there is a relationship between \(f\) and \(\lambda\); the higher the frequency, the smaller the wavelength (Figure \(\PageIndex{7}\)).

Example \(\PageIndex{1}\): Calculating Wavelengths

Calculate the wavelengths of sounds at the extremes of the audible range, 20 and 20,000 Hz, in 30.0 °C air. (Assume that the frequency values are accurate to two significant figures.)

To find wavelength from frequency, we can use \(v = f \lambda\).

• Identify knowns. The value for \(v\) is given by \[v = 331\; m/s \sqrt{\frac{T}{273\; K}} \ldotp \nonumber\]
• Convert the temperature into kelvins and then enter the temperature into the equation \[v = 331\; m/s \sqrt{\frac{303\; K}{273\; K}} = 348.7\; m/s \ldotp \nonumber\]
• Solve the relationship between speed and wavelength for \(\lambda\): $$\lambda = \frac{v}{f} \ldotp \nonumber$$
• Enter the speed and the minimum frequency to give the maximum wavelength: \[\lambda_{max} = \frac{348.7\; m/s}{20\; Hz} = 17\; m \ldotp \nonumber\]
• Enter the speed and the maximum frequency to give the minimum wavelength: \[\lambda_{min} = \frac{348.7\; m/s}{20,000\; Hz} = 0.017\; m = 1.7\; cm \ldotp \nonumber\]

Significance

Because the product of \(f\) multiplied by \(\lambda\) equals a constant, the smaller \(f\) is, the larger \(\lambda\) must be, and vice versa.

The speed of sound can change when sound travels from one medium to another, but the frequency usually remains the same. This is similar to the frequency of a wave on a string being equal to the frequency of the force oscillating the string. If \(v\) changes and \(f\) remains the same, then the wavelength \(\lambda\) must change. That is, because \(v = f \lambda\), the higher the speed of a sound, the greater its wavelength for a given frequency.

Exercise \(\PageIndex{1}\)

Imagine you observe two firework shells explode. You hear the explosion of one as soon as you see it. However, you see the other shell for several milliseconds before you hear the explosion. Explain why this is so.

Although sound waves in a fluid are longitudinal, sound waves in a solid travel both as longitudinal waves and transverse waves. Seismic waves, which are essentially sound waves in Earth’s crust produced by earthquakes, are an interesting example of how the speed of sound depends on the rigidity of the medium. Earthquakes produce both longitudinal and transverse waves, and these travel at different speeds. The bulk modulus of granite is greater than its shear modulus. For that reason, the speed of longitudinal or pressure waves (P-waves) in earthquakes in granite is significantly higher than the speed of transverse or shear waves (S-waves). Both types of earthquake waves travel slower in less rigid material, such as sediments. P-waves have speeds of 4 to 7 km/s, and S-waves range in speed from 2 to 5 km/s, both being faster in more rigid material. The P-wave gets progressively farther ahead of the S-wave as they travel through Earth’s crust. The time between the P- and S-waves is routinely used to determine the distance to their source, the epicenter of the earthquake. Because S-waves do not pass through the liquid core, two shadow regions are produced (Figure \(\PageIndex{8}\)).

As sound waves move away from a speaker, or away from the epicenter of an earthquake, their power per unit area decreases. This is why the sound is very loud near a speaker and becomes less loud as you move away from the speaker. This also explains why there can be an extreme amount of damage at the epicenter of an earthquake but only tremors are felt in areas far from the epicenter. The power per unit area is known as the intensity, and in the next section, we will discuss how the intensity depends on the distance from the source.

13.1 Types of Waves

Section learning objectives.

By the end of this section, you will be able to do the following:

• Define mechanical waves and medium, and relate the two
• Distinguish a pulse wave from a periodic wave
• Distinguish a longitudinal wave from a transverse wave and give examples of such waves

Teacher Support

The learning objectives in this section will help your students master the following standards:

• (A) examine and describe oscillatory motion and wave propagation in various types of media.

Section Key Terms

Mechanical waves.

What do we mean when we say something is a wave? A wave is a disturbance that travels or propagates from the place where it was created. Waves transfer energy from one place to another, but they do not necessarily transfer any mass. Light, sound, and waves in the ocean are common examples of waves. Sound and water waves are mechanical waves ; meaning, they require a medium to travel through. The medium may be a solid, a liquid, or a gas, and the speed of the wave depends on the material properties of the medium through which it is traveling. However, light is not a mechanical wave; it can travel through a vacuum such as the empty parts of outer space.

A familiar wave that you can easily imagine is the water wave. For water waves, the disturbance is in the surface of the water, an example of which is the disturbance created by a rock thrown into a pond or by a swimmer splashing the water surface repeatedly. For sound waves, the disturbance is caused by a change in air pressure, an example of which is when the oscillating cone inside a speaker creates a disturbance. For earthquakes, there are several types of disturbances, which include the disturbance of Earth’s surface itself and the pressure disturbances under the surface. Even radio waves are most easily understood using an analogy with water waves. Because water waves are common and visible, visualizing water waves may help you in studying other types of waves, especially those that are not visible.

Water waves have characteristics common to all waves, such as amplitude , period , frequency , and energy , which we will discuss in the next section.

Misconception Alert

Many people think that water waves push water from one direction to another. In reality, however, the particles of water tend to stay in one location only, except for moving up and down due to the energy in the wave. The energy moves forward through the water, but the water particles stay in one place. If you feel yourself being pushed in an ocean, what you feel is the energy of the wave, not the rush of water. If you put a cork in water that has waves, you will see that the water mostly moves it up and down.

[BL] [OL] [AL] Ask students to give examples of mechanical and nonmechanical waves.

Pulse Waves and Periodic Waves

If you drop a pebble into the water, only a few waves may be generated before the disturbance dies down, whereas in a wave pool, the waves are continuous. A pulse wave is a sudden disturbance in which only one wave or a few waves are generated, such as in the example of the pebble. Thunder and explosions also create pulse waves. A periodic wave repeats the same oscillation for several cycles, such as in the case of the wave pool, and is associated with simple harmonic motion. Each particle in the medium experiences simple harmonic motion in periodic waves by moving back and forth periodically through the same positions.

[BL] Any kind of wave, whether mechanical or nonmechanical, or transverse or longitudinal, can be in the form of a pulse wave or a periodic wave.

Consider the simplified water wave in Figure 13.2 . This wave is an up-and-down disturbance of the water surface, characterized by a sine wave pattern. The uppermost position is called the crest and the lowest is the trough . It causes a seagull to move up and down in simple harmonic motion as the wave crests and troughs pass under the bird.

Longitudinal Waves and Transverse Waves

Mechanical waves are categorized by their type of motion and fall into any of two categories: transverse or longitudinal. Note that both transverse and longitudinal waves can be periodic. A transverse wave propagates so that the disturbance is perpendicular to the direction of propagation. An example of a transverse wave is shown in Figure 13.3 , where a woman moves a toy spring up and down, generating waves that propagate away from herself in the horizontal direction while disturbing the toy spring in the vertical direction.

In contrast, in a longitudinal wave , the disturbance is parallel to the direction of propagation. Figure 13.4 shows an example of a longitudinal wave, where the woman now creates a disturbance in the horizontal direction—which is the same direction as the wave propagation—by stretching and then compressing the toy spring.

Tips For Success

Longitudinal waves are sometimes called compression waves or compressional waves , and transverse waves are sometimes called shear waves .

Teacher Demonstration

Transverse and longitudinal waves may be demonstrated in the class using a spring or a toy spring, as shown in the figures.

Waves may be transverse, longitudinal, or a combination of the two . The waves on the strings of musical instruments are transverse (as shown in Figure 13.5 ), and so are electromagnetic waves, such as visible light. Sound waves in air and water are longitudinal. Their disturbances are periodic variations in pressure that are transmitted in fluids.

Sound in solids can be both longitudinal and transverse. Essentially, water waves are also a combination of transverse and longitudinal components, although the simplified water wave illustrated in Figure 13.2 does not show the longitudinal motion of the bird.

Earthquake waves under Earth’s surface have both longitudinal and transverse components as well. The longitudinal waves in an earthquake are called pressure or P-waves, and the transverse waves are called shear or S-waves. These components have important individual characteristics; for example, they propagate at different speeds. Earthquakes also have surface waves that are similar to surface waves on water.

Energy propagates differently in transverse and longitudinal waves. It is important to know the type of the wave in which energy is propagating to understand how it may affect the materials around it.

Watch Physics

Introduction to waves.

This video explains wave propagation in terms of momentum using an example of a wave moving along a rope. It also covers the differences between transverse and longitudinal waves, and between pulse and periodic waves.

• After a compression wave, some molecules move forward temporarily.
• After a compression wave, some molecules move backward temporarily.
• After a compression wave, some molecules move upward temporarily.
• After a compression wave, some molecules move downward temporarily.

Fun In Physics

The physics of surfing.

Many people enjoy surfing in the ocean. For some surfers, the bigger the wave, the better. In one area off the coast of central California, waves can reach heights of up to 50 feet in certain times of the year ( Figure 13.6 ).

How do waves reach such extreme heights? Other than unusual causes, such as when earthquakes produce tsunami waves, most huge waves are caused simply by interactions between the wind and the surface of the water. The wind pushes up against the surface of the water and transfers energy to the water in the process. The stronger the wind, the more energy transferred. As waves start to form, a larger surface area becomes in contact with the wind, and even more energy is transferred from the wind to the water, thus creating higher waves. Intense storms create the fastest winds, kicking up massive waves that travel out from the origin of the storm. Longer-lasting storms and those storms that affect a larger area of the ocean create the biggest waves since they transfer more energy. The cycle of the tides from the Moon’s gravitational pull also plays a small role in creating waves.

Actual ocean waves are more complicated than the idealized model of the simple transverse wave with a perfect sinusoidal shape. Ocean waves are examples of orbital progressive waves , where water particles at the surface follow a circular path from the crest to the trough of the passing wave, then cycle back again to their original position. This cycle repeats with each passing wave.

As waves reach shore, the water depth decreases and the energy of the wave is compressed into a smaller volume. This creates higher waves—an effect known as shoaling .

Since the water particles along the surface move from the crest to the trough, surfers hitch a ride on the cascading water, gliding along the surface. If ocean waves work exactly like the idealized transverse waves, surfing would be much less exciting as it would simply involve standing on a board that bobs up and down in place, just like the seagull in the previous figure.

Additional information and illustrations about the scientific principles behind surfing can be found in the “Using Science to Surf Better!” video.

• The surfer would move side-to-side/back-and-forth vertically with no horizontal motion.
• The surfer would forward and backward horizontally with no vertical motion.

Check Your Understanding

Use these questions to assess students’ achievement of the section’s Learning Objectives. If students are struggling with a specific objective, these questions will help identify such objective and direct them to the relevant content.

• A wave is a force that propagates from the place where it was created.
• A wave is a disturbance that propagates from the place where it was created.
• A wave is matter that provides volume to an object.
• A wave is matter that provides mass to an object.
• No, electromagnetic waves do not require any medium to propagate.
• No, mechanical waves do not require any medium to propagate.
• Yes, both mechanical and electromagnetic waves require a medium to propagate.
• Yes, all transverse waves require a medium to travel.
• A pulse wave is a sudden disturbance with only one wave generated.
• A pulse wave is a sudden disturbance with only one or a few waves generated.
• A pulse wave is a gradual disturbance with only one or a few waves generated.
• A pulse wave is a gradual disturbance with only one wave generated.

What are the categories of mechanical waves based on the type of motion?

• Both transverse and longitudinal waves
• Only longitudinal waves
• Only transverse waves
• Only surface waves

In which direction do the particles of the medium oscillate in a transverse wave?

• Perpendicular to the direction of propagation of the transverse wave
• Parallel to the direction of propagation of the transverse wave

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How do sound waves work?

Sound waves are vibrations that can move us, hurt us, and maybe even heal us.

By Brian S. Hawkins | Updated Jun 1, 2023 2:00 PM EDT

We live our entire lives surrounded by them. They slam into us constantly at more than 700 miles per hour, sometimes hurting, sometimes soothing . They have the power to communicate ideas, evoke fond memories, start fights, entertain an audience, scare the heck out of us, or help us fall in love. They can trigger a range of emotions and they even cause physical damage. This reads like something out of science fiction , but what we’re talking about is very much real and already part of our day-to-day lives. They’re sound waves. So, what are sound waves and how do they work?

If you’re not in the industry of audio, you probably don’t think too much about the mechanics of sound. Sure, most people care about how sounds make them feel, but they aren’t as concerned with how the sound actually affects them. Understanding how sound works does have a number of practical applications , however, and you don’t have to be a physicist or engineer to explore this fascinating subject. Here’s a primer on the science of sound to help get you started.

What’s in a wave

When energy moves through a substance such as water or air, it makes a wave. There are two kinds of waves: longitudinal ones and transverse ones. Transverse waves, as NASA notes , are probably what most people think of when they picture waves—like the up-down ripples of a battle rope used to work out. Longitudinal waves are also known as compression waves, and that’s what sound waves are. There’s no perpendicular motion to these, rather, the wave moves in the same direction as the disturbance.

How sound waves work

Sound waves are a type of energy that’s released when an object vibrates. Those acoustic waves travel from their source through air or another medium, and when they come into contact with our eardrums, our brains translate the pressure waves into words, music, or signals we can understand. These pulses help you place where things are in your environment.

We can experience sound waves in ways that are more physical, not just physiological, too. If sound waves reach  a microphone —whether it’s a plug-n-play  USB livestream mic  or a studio-quality  microphone for vocals —it transforms them into electronic impulses that are turned back into sound by vibrating speakers . Whether listening at home or at a concert, we can feel the deep bass in our chest. Opera singers can use them to shatter glass. It’s even possible to see sound waves sent through a medium like sand, which leaves behind a kind of sonic footprint. 

That shape is rolling peaks and valleys, the signature of a sine (aka sinusoid) wave. If the wave travels faster, those peaks and valleys form closer together. If it moves slower, they spread out. It’s not a poor analogy to think of them somewhat like waves in the ocean. It’s this movement that allows sound waves to do so many other things. 

It’s all about frequency

When we talk about a sound wave’s speed, we’re referring to how fast these longitudinal waves move from peak to trough and back to peak. Up … and then down … and then up … and then down. The technical term is frequency , but many of us know it as pitch. We measure sound frequency in hertz (Hz), which represents cycles-per-second, with faster frequencies creating higher-pitched sounds. For instance, the A note right above Middle C on a piano is measured at 440 Hz—it travels up and down at 440 cycles per second. Middle C itself is 261.63 Hz—a lower pitch, vibrating at a slower frequency.

Understanding frequencies can be useful in many ways. You can precisely tune an instrument by analyzing the frequencies of its strings. Recording engineers use their understanding of frequency ranges to dial in equalization settings that help sculpt the sound of the music they’re mixing . Car designers work with frequencies—and materials that can block them—to help make engines quieter. And  active noise cancellation  uses artificial intelligence and algorithms to measure external frequencies and generate inverse waves to cancel environmental rumble and hum, allowing top-tier ANC headphones and earphones to isolate the wearer from the noise around them. The average frequency range of human hearing is 20 to 20,000 Hz.

What’s in a name? 

The hertz measurement is named for the German physicist Heinrich Rudolf Hertz , who proved the existence of electromagnetic waves. 

Getting amped

Amplitude equates to sound’s volume or intensity. Using our ocean analogy—because, hey, it works—amplitude describes the height of the waves.

We measure amplitude in decibels (dB). The dB scale is logarithmic, which means there’s a fixed ratio between measurement units. And what does that mean? Let’s say you have a dial on your guitar amp with evenly spaced steps on it numbered one through five. If the knob is following a logarithmic scale, the volume won’t increase evenly as you turn the dial from marker to marker. If the ratio is 4, let’s say, then turning the dial from the first to the second marker increases the sound by 4 dB. But going from the second to the third marker increases it by 16 dB. Turn the dial again and your amp becomes 64 dB louder. Turn it once more, and you’ll blast out a blistering 256 dB—more than loud enough to rupture your eardrums. But if you’re somehow still standing, you can turn that knob one more time to increase your volume to a brain-walloping 1,024 decibels. That’s almost 10 times louder than any rock concert you’ll ever encounter, and it will definitely get you kicked out of your rehearsal space. All of which is why real amps aren’t designed that way.

Twice as nice

We interpret a 10 dB increase in amplitude as a doubling of volume. 

Parts of a sound wave

Timbre and envelope are two characteristics of sound waves that help determine why, say, two instruments can play the same chords but sound nothing alike. 

Timbre is determined by the unique harmonics formed by the combination of notes in a chord. The A in an A chord is only its fundamental note—you also have overtones and undertones. The way these sound together helps keep a piano from sounding like a guitar, or an angry grizzly bear from sounding like a rumbling tractor engine. 

[Related: Even plants pick up on good vibes ]

But we also rely on envelopes, which determine how a sound’s amplitude changes over time. A cello’s note might swell slowly to its maximum volume, then hold for a bit before gently fading out again. On the other hand, a slamming door delivers a quick, sharp, loud sound that cuts off almost instantly. Envelopes comprise four parts: Attack, Decay, Sustain, and Release. In fact, they’re more formally known as ADSR Envelopes. 

• Attack: This is how quickly the sound achieves its maximum volume. A barking dog has a very short attack; a rising orchestra has a slower one. 
• Decay: This describes how fast the sound settles into its sustained volume. When a guitar player plucks a string , the note starts off loudly but quickly settles into something quieter before fading out completely. The time it takes to hit that sustained volume is decay. 
• Sustain: Sustain isn’t a measure of time; it’s a measure of amplitude, or volume. It’s how loud the plucked guitar note is after the initial attack but before it fades out. 
• Release: This is the time it takes for the note to drift off to silence. 

Speed of sound

Science fiction movies like it when spaceships explode with giant, rumbling, surround-sound booms . However, sound needs to travel through a medium so, despite Hollywood saying otherwise, you’d never hear an explosion in the vacuum of space. 

Sound’s velocity , or the speed it travels at , differs depending on the density (and even temperature) of the medium it’s moving through—it’s faster in the air than water, for instance. Generally, sound moves at 1,127 feet per second, or 767.54 miles per hour. When jets break the sound barrier , they’re traveling faster than that. And knowing these numbers lets you estimate the distance of a lightning strike by counting the time between the flash and thunder’s boom—if you count to 10, it’s approximately 11,270 feet away, or about a quarter-mile. (Very roughly, of course.) 

A stimulating experience

Anyone can benefit from understanding the fundamentals of sound and what sound waves are. Musicians and content creators with home recording set-ups and studio monitors obviously need a working knowledge of frequencies and amplitude. If you host a podcast, you’ll want as many tools as possible to ensure your voice sounds clear and rich, and this can include understanding the frequencies of your voice, what microphones are best suited to them , and how to set up your room to reflect or dampen the sounds you do or do not want. Having some foundational information is also useful when doing home-improvement projects— when treating a recording workstation , for instance, or just soundproofing a new enclosed deck. And who knows, maybe one day you’ll want to shatter glass. Having a better understanding of the physics of sound opens up wonderful new ways to explore and experience the world around us. Now, go out there and make some noise!

This post has been updated. It was originally published on July 27, 2021.

Brian is a documentary producer, director, and cameraman on feature films and docu-series, and has more than 20 years’ experience as a journalist. He enjoys covering pop-culture, tech, and the conflation of the two.

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Anatomy of an Electromagnetic Wave

Energy, a measure of the ability to do work, comes in many forms and can transform from one type to another. Examples of stored or potential energy include batteries and water behind a dam. Objects in motion are examples of kinetic energy. Charged particles—such as electrons and protons—create electromagnetic fields when they move, and these fields transport the type of energy we call electromagnetic radiation, or light.

What are Electromagnetic and Mechanical waves?

Mechanical waves and electromagnetic waves are two important ways that energy is transported in the world around us. Waves in water and sound waves in air are two examples of mechanical waves. Mechanical waves are caused by a disturbance or vibration in matter, whether solid, gas, liquid, or plasma. Matter that waves are traveling through is called a medium. Water waves are formed by vibrations in a liquid and sound waves are formed by vibrations in a gas (air). These mechanical waves travel through a medium by causing the molecules to bump into each other, like falling dominoes transferring energy from one to the next. Sound waves cannot travel in the vacuum of space because there is no medium to transmit these mechanical waves.

ELECTROMAGNETIC WAVES

Electricity can be static, like the energy that can make your hair stand on end. Magnetism can also be static, as it is in a refrigerator magnet. A changing magnetic field will induce a changing electric field and vice-versa—the two are linked. These changing fields form electromagnetic waves. Electromagnetic waves differ from mechanical waves in that they do not require a medium to propagate. This means that electromagnetic waves can travel not only through air and solid materials, but also through the vacuum of space.

In the 1860's and 1870's, a Scottish scientist named James Clerk Maxwell developed a scientific theory to explain electromagnetic waves. He noticed that electrical fields and magnetic fields can couple together to form electromagnetic waves. He summarized this relationship between electricity and magnetism into what are now referred to as "Maxwell's Equations."

Heinrich Hertz, a German physicist, applied Maxwell's theories to the production and reception of radio waves. The unit of frequency of a radio wave -- one cycle per second -- is named the hertz, in honor of Heinrich Hertz.

His experiment with radio waves solved two problems. First, he had demonstrated in the concrete, what Maxwell had only theorized — that the velocity of radio waves was equal to the velocity of light! This proved that radio waves were a form of light! Second, Hertz found out how to make the electric and magnetic fields detach themselves from wires and go free as Maxwell's waves — electromagnetic waves.

WAVES OR PARTICLES? YES!

Light is made of discrete packets of energy called photons. Photons carry momentum, have no mass, and travel at the speed of light. All light has both particle-like and wave-like properties. How an instrument is designed to sense the light influences which of these properties are observed. An instrument that diffracts light into a spectrum for analysis is an example of observing the wave-like property of light. The particle-like nature of light is observed by detectors used in digital cameras—individual photons liberate electrons that are used for the detection and storage of the image data.

POLARIZATION

One of the physical properties of light is that it can be polarized. Polarization is a measurement of the electromagnetic field's alignment. In the figure above, the electric field (in red) is vertically polarized. Think of a throwing a Frisbee at a picket fence. In one orientation it will pass through, in another it will be rejected. This is similar to how sunglasses are able to eliminate glare by absorbing the polarized portion of the light.

DESCRIBING ELECTROMAGNETIC ENERGY

The terms light, electromagnetic waves, and radiation all refer to the same physical phenomenon: electromagnetic energy. This energy can be described by frequency, wavelength, or energy. All three are related mathematically such that if you know one, you can calculate the other two. Radio and microwaves are usually described in terms of frequency (Hertz), infrared and visible light in terms of wavelength (meters), and x-rays and gamma rays in terms of energy (electron volts). This is a scientific convention that allows the convenient use of units that have numbers that are neither too large nor too small.

The number of crests that pass a given point within one second is described as the frequency of the wave. One wave—or cycle—per second is called a Hertz (Hz), after Heinrich Hertz who established the existence of radio waves. A wave with two cycles that pass a point in one second has a frequency of 2 Hz.

Electromagnetic waves have crests and troughs similar to those of ocean waves. The distance between crests is the wavelength. The shortest wavelengths are just fractions of the size of an atom, while the longest wavelengths scientists currently study can be larger than the diameter of our planet!

An electromagnetic wave can also be described in terms of its energy—in units of measure called electron volts (eV). An electron volt is the amount of kinetic energy needed to move an electron through one volt potential. Moving along the spectrum from long to short wavelengths, energy increases as the wavelength shortens. Consider a jump rope with its ends being pulled up and down. More energy is needed to make the rope have more waves.

Next: Wave Behaviors

National Aeronautics and Space Administration, Science Mission Directorate. (2010). Anatomy of an Electromagnetic Wave. Retrieved [insert date - e.g. August 10, 2016] , from NASA Science website: http://science.nasa.gov/ems/02_anatomy

Science Mission Directorate. "Anatomy of an Electromagnetic Wave" NASA Science . 2010. National Aeronautics and Space Administration. [insert date - e.g. 10 Aug. 2016] http://science.nasa.gov/ems/02_anatomy

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Understanding Sound Waves and How They Work

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Sound. When a drum is struck, the drumhead vibrates and the vibrations are transmitted through the air in the form of sound waves . When they strike the ear, these waves produce the sensation of sound.

Technically, sound is defined as a mechanical disturbance traveling through an elastic medium — a material that tends to return to its original condition after being deformed. The medium doesn't have to be air. Metal, wood, stone, glass, water, and many other substances conduct sound — many of them even better than air.

The Basics of Sound

Sound waves, speed of sound, the behavior of a sound wave, sound quality, history of sound.

There are many sources of sound. Familiar kinds include the vibration of a person's vocal cords, vibrating strings (piano, violin), a vibrating column of air (trumpet, flute), and vibrating solids (a door when someone knocks). It's impossible to list them all because anything that imparts a disturbance to an elastic medium is a source of sound.

Sound can be described in terms of pitch — from the low rumble of distant thunder to the high-pitched buzzing of a mosquito — and loudness. Pitch and loudness , however, are subjective qualities; they depend in part on the hearer's sense of hearing. Objective, measurable qualities of sound include frequency and intensity, which are related to pitch and loudness. These terms, as well as others used in discussing sound, are best understood through an examination of sound waves and their behavior.

Speed of sound in various mediums

Air, like all matter, consists of molecules. Even a tiny region of air contains vast numbers of air molecules. The molecules are in constant motion, traveling randomly and at great speed. They constantly collide with and rebound from one another and strike and rebound from objects that are in contact with the air.

When an object vibrates it produces sound waves in the air. For example, when the head of a drum is hit with a mallet, the drumhead vibrates and produces sound waves. The vibrating drumhead produces sound waves because it moves alternately outward and inward, pushing against, then moving away from, the air next to it. The air particles that strike the drumhead while it is moving outward rebound from it with more than their normal energy and speed, having received a push from the drumhead.

These faster-moving molecules move into the surrounding air. For a moment, the region next to the drumhead has a greater-than-normal concentration of air molecules — it becomes a region of compression. As the faster-moving molecules overtake the air molecules in the surrounding air, they collide with them and pass on their extra energy. The region of compression moves outward as the energy from the vibrating drumhead is transferred to groups of molecules farther and farther away.

Air molecules that strike the drumhead while it's moving inward rebound from it with less than their normal energy and speed. For a moment, the region next to the drumhead has fewer air molecules than normal — it becomes a region of rarefaction. Molecules colliding with these slower-moving molecules also rebound with less speed than normal, and the region of rarefaction travels outward.

The nature of sound is captured through its fundamental characteristics : wavelength (the distance between wave peaks), amplitude (the height of the wave, corresponding to loudness), frequency (the number of waves passing a point per second, related to pitch), time period (the time it takes for one complete wave cycle to occur), and velocity (the speed at which the wave travels through a medium). These properties intertwine to craft the unique signature of every sound we hear.

The wave nature of sound becomes apparent when a graph is drawn to show the changes in the concentration of air molecules at some point as the alternating pulses of compression and rarefaction pass that point. The graph for a single pure tone, such as that produced by a vibrating tuning fork, would show a sine wave (illustrated here ). The curve shows the changes in concentration. It begins, arbitrarily, at some time when the concentration is normal and a compression pulse is just arriving. The distance of each point on the curve from the horizontal axis indicates how much the concentration varies from normal.

Each compression and the following rarefaction make up one cycle. (A cycle can also be measured from any point on the curve to the next corresponding point.) The frequency of a sound is measured in cycles per second or hertz (abbreviated Hz). The amplitude is the greatest amount by which the concentration of air molecules varies from the normal.

The wavelength of a sound is the distance the disturbance travels during one cycle. It's related to the sound's speed and frequency by the formula speed/frequency = wavelength. This means that high-frequency sounds have short wavelengths and low-frequency sounds have long wavelengths. The human ear can detect sounds with frequencies as low as 20 Hz and as high as 20,000 Hz. In still air at room temperature, sounds with these frequencies have wavelengths of 75 feet (23 m) and 0.68 inch (1.7 cm) respectively.

Intensity refers to the amount of energy transmitted by the disturbance. It's proportional to the square of the amplitude. Intensity is measured in watts per square centimeter or in decibels (db). The decibel scale is defined as follows: An intensity of 10-16 watts per square centimeter equals 0 db. (Written out in decimal form, 10-16 appears as 0.0000000000000001.) Each tenfold increase in watts per square centimeter means an increase of 10 db. Thus, an intensity of 10-15 watts per square centimeter can also be expressed as 10 db and an intensity of 10-4 (or 0.0001) watts per square centimeter as 120 db.

The intensity of sound drops rapidly with increasing distance from the source. For a small sound source radiating energy uniformly in all directions, intensity varies inversely with the square of the distance from the source. That is, at a distance of two feet from the source the intensity is one-fourth as great as it is at a distance of one foot; at three feet it is only one-ninth as great as at one foot, etc.

Pitch depends on the frequency ; in general, a rise in frequency causes a sensation of rising pitch. The ability to distinguish between two sounds that are close in frequency, however, decreases in the upper and lower parts of the audible frequency range. There is also variation from person to person in the ability to distinguish between two sounds of very nearly the same frequency. Some trained musicians can detect differences in frequency as small as 1 or 2 Hz.

Because of how the hearing mechanism functions, the perception of pitch is also affected by intensity. Thus, when a tuning fork vibrating at 440 Hz (the frequency of A above middle C on the piano) is brought closer to the ear, a slightly lower tone, as though the fork were vibrating more slowly, is heard.

When the source of a sound is moving at a relatively high speed, a stationary listener hears a sound higher in pitch when the source is moving toward him or her and a sound lower in pitch when the source is moving away. This phenomenon, known as the Doppler effect , is due to the wave nature of sound.

In general, an increase in intensity will cause a sensation of increased loudness. But loudness does not increase in direct proportion to intensity. A sound of 50 dB has ten times the intensity of a sound of 40 dB but is only twice as loud. Loudness doubles with each increase of 10 dB in intensity.

Loudness is also affected by frequency because the human ear is more sensitive to some frequencies than to others. The threshold of hearing — the lowest sound intensity that will produce the sensation of hearing for most people — is about 0 dB in the 2,000 to 5,000 Hz frequency range. For frequencies below and above this range, sounds must have greater intensity to be heard. Thus, for example, a sound of 100 Hz is barely audible at 30 dB; a sound of 10,000 Hz is barely audible at 20 dB. At 120 to 140 dB, most people experience physical discomfort or actual pain, and this level of intensity is referred to as the threshold of pain .

When we visualize waves, we often think of transverse waves — like the rolling waves on a beach — where the motion of the wave is perpendicular to the direction of energy transfer. However, sound waves are a different type altogether — a longitudinal wave. In longitudinal sound waves, such as sound waves produced by a vibrating drumhead or our vocal cords, the particles of the medium move parallel to the wave's direction of travel. This movement creates areas of compression and rarefaction in the medium — be it air, water, or a solid — which our ears interpret as sound. Understanding the difference between longitudinal and transverse waves is central to understanding sound.

The speed of sound depends on the elasticity and density of the medium through which it is traveling. In general, sound travels faster in liquids than in gases and faster in solids than in liquids. The greater the elasticity and the lower the density, the faster sound moves in a medium. The mathematical relationship is speed = (elasticity/density).

The effect of elasticity and density on the speed of sound can be seen by comparing the speed of sound in air, hydrogen, and iron. Air and hydrogen have nearly the same elastic properties, but the density of hydrogen is less than that of air. Sound travels faster (about 4 times as fast) in hydrogen than in air. Although the density of air is much less than that of iron, the elasticity of iron is very much greater than that of air. Sound travels faster (about 14 times as fast) in iron than in air.

The speed of sound in a material, particularly in a gas or liquid, varies with temperature because a change in temperature affects the material's density. In air, for example, the speed of sound increases with an increase in temperature . At 32 °F. (0 °C.), the speed of sound in air is 1,087 feet per second (331 m/s); at 68 °F. (20 °C.), it is 1,127 feet per second (343 m/s).

The terms subsonic and supersonic refer to the speed of an object, such as an airplane, in relation to the speed of sound in the surrounding air. A subsonic speed is below the speed of sound; a supersonic speed is above the speed of sound. An object traveling at supersonic speed produces shock waves rather than ordinary sound waves. A shock wave is a compression wave that, when produced in air, can usually be heard as a sonic boom .

The speeds of supersonic objects are often expressed in terms of Mach number — the ratio of the object's speed to the speed of sound in the surrounding air. Thus, an object traveling at Mach 1 is traveling at the speed of sound; at Mach 2, it is traveling at twice the speed of sound.

Like light waves and other waves, sound waves are reflected, refracted, and diffracted, and exhibit interference.

Sound is constantly being reflected off many different surfaces. Most of the time the reflected sound is not noticed, because two identical sounds that reach the human ear less than 1/15 of a second apart cannot be distinguished as separate sounds. When the reflected sound is heard separately, it's called an echo .

Sound is reflected from a surface at the same angle at which it strikes the surface. This fact makes it possible to focus sound by means of curved reflecting surfaces in the same way that curved mirrors can be used to focus light. It also accounts for the effects of so-called whispering galleries, rooms in which a word whispered at one point can be heard distinctly at some other point fairly far away, though it cannot be heard anywhere else in the room. (The National Statuary Hall of the United States Capitol is an example.) Reflection is also used to focus sound in a megaphone and when calling through cupped hands.

The reflection of sound can pose a serious problem in concert halls and auditoriums. In a poorly designed hall, a speaker's first word may reverberate (echo repeatedly) for several seconds, so that the listeners may hear all the words of a sentence echoing at the same time. Music can be similarly distorted. Such problems can usually be corrected by covering reflecting surfaces with sound-absorbing materials such as draperies or acoustical tiles. Clothing also absorbs sound; for this reason, reverberation is greater in an empty hall than in one filled with people. All these sound-absorbing materials are porous; sound waves entering the tiny air-filled spaces bounce around in them until their energy is spent. They are, in effect, trapped.

The reflection of sound is used by some animals, notably bats , for echolocation — locating, and in some cases identifying, objects through the sense of hearing rather than the sense of sight. Bats emit bursts of sound of frequencies far beyond the upper limits of human hearing. Sounds with short wavelengths are reflected even from very small objects. A bat can unerringly locate and catch even a mosquito in total darkness. Sonar is an artificial form of echolocation .

When a wave passes from one material to another at an angle, it usually changes speed, causing the wave front to bend. The refraction of sound can be demonstrated in a physics laboratory by using a lens-shaped balloon filled with carbon dioxide to bring sound waves to a focus.

Diffraction

When sound waves pass around an obstacle or through an opening in an obstacle, the edge of the obstacle or the opening acts as a secondary sound source, sending out waves of the same frequency and wavelength (but of lower intensity) as the original source. The spreading out of sound waves from the secondary source is called diffraction . Because of this phenomenon, sound can be heard around corners despite the fact that sound waves generally travel in a straight line.

Interference

Whenever waves interact, interference occurs. For sound waves, the phenomenon is perhaps best understood by thinking in terms of the compressions and rarefactions of the two waves as they arrive at some point. When the waves are in phase so that their compressions and rarefactions coincide, they reinforce each other ( constructive interference ). When they are out of phase, so that the compressions of one coincide with the rarefactions of the other, they tend to weaken or even cancel each other ( destructive interference ). The interaction between the two waves produces a resultant wave.

In auditoriums, destructive interference between sound from the stage and sound reflected from other parts of the hall can create dead spots in which both the volume and clarity of sound are poor. Such interference can be reduced by the use of sound-absorbing materials on reflecting surfaces. On the other hand, interference can improve an auditorium's acoustical qualities. This is done by arranging the reflecting surfaces in such a way that the level of sound is actually increased in the area in which the audience sits.

Interference between two waves of nearly but not quite equal frequencies produces a tone of alternately increasing and decreasing intensity because the two waves continually fall in and out of phase. The pulsations heard are called beats. Piano tuners make use of this effect, adjusting the tone of a string against that of a standard tuning fork until beats can no longer be heard.

Sound waves are fundamentally pressure waves, traveling through the compression and rarefaction of particles within a medium. Sound waves consist of areas where particles are bunched together, followed by areas where they're spread apart. These high-pressure and low-pressure regions propagate through environments such as air, water or solids, as the energy of the sound wave moves from particle to particle. It's the rapid variation in pressure that an ear drum detects and the brain decodes into the sounds we hear.

Sounds of a single pure frequency are produced only by tuning forks and electronic devices called oscillators ; most sounds are a mixture of tones of different frequencies and amplitudes. The tones produced by musical instruments have one important characteristic in common: they are periodic, that is, the vibrations occur in a repeating pattern. The oscilloscope trace of a trumpet's sound shows such a pattern. For most non-musical sounds, such as those of a bursting balloon or a person coughing, an oscilloscope trace would show a jagged, irregular pattern, indicating a jumble of frequencies and amplitudes.

A column of air, as that in a trumpet, and a piano string both have a fundamental frequency — the frequency at which they vibrate most readily when set in motion. For a vibrating column of air, that frequency is determined principally by the length of the column. (The trumpet's valves are used to change the effective length of the column.) For a vibrating string, the fundamental frequency depends on the string's length, its tension, and its mass per unit length.

In addition to its fundamental frequency, a string or vibrating column of air also produces overtones with frequencies that are whole-number multiples of the fundamental frequency. It is the number of overtones produced and their relative strength that gives a musical tone from a given source its distinctive quality or timbre . The addition of further overtones would produce a complicated pattern, such as that of the oscilloscope trace of the trumpet's sound.

How the fundamental frequency of a vibrating string depends on the string's length, tension, and mass per unit length is described by three laws:

1. The fundamental frequency of a vibrating string is inversely proportional to its length.

Reducing the length of a vibrating string by one-half will double its frequency, raising the pitch by one octave, if the tension remains the same.

2. The fundamental frequency of a vibrating string is directly proportional to the square root of the tension.

Increasing the tension of a vibrating string raises the frequency; if the tension is made four times as great, the frequency is doubled, and the pitch is raised by one octave.

3. The fundamental frequency of a vibrating string is inversely proportional to the square root of the mass per unit length.

This means that of two strings of the same material and with the same length and tension, the thicker string has the lower fundamental frequency. If the mass per unit length of one string is four times that of the other, the thicker string has a fundamental frequency one-half that of the thinner string and produces a tone one octave lower.

One of the first discoveries regarding sound was made in the sixth century B.C. by the Greek mathematician and philosopher Pythagoras . He noted the relationship between the length of a vibrating string and the tone it produces — what is now known as the first law of strings. Pythagoras may also have understood that the sensation of sound is caused by vibrations. Not long after his time it was recognized that this sensation depends on vibrations traveling through the air and striking the eardrum.

About 1640 the French mathematician Marin Mersenne conducted the first experiments to determine the speed of sound in air. Mersenne is also credited with discovering the second and third laws of strings. In 1660 the British scientist Robert Boyle demonstrated that the transmission of sound required a medium — by showing that the ringing of a bell in a jar from which the air had been pumped could not be heard.

Ernst Chladni , a German physicist, made extensive analyses of sound vibrations during the late 1700s and early 1800s. In the early 1800s, the French mathematician Fourier discovered that such complex waves as those produced by a vibrating string with all its overtones consist of a series of simple periodic waves.

An important contribution to the understanding of acoustics was made by Wallace Clement Sabine , a physicist at Harvard University, in the late 1890s. Sabine was asked to improve the acoustics of the main lecture hall in Harvard's Fogg Art Museum. He was first to measure reverberation time — which he found to be 5 1/2 seconds in the lecture hall. Experimenting first with seat cushions from a nearby theater, and later with other sound-absorbing materials and other methods, Sabine laid the foundation for architectural acoustics. He designed Boston Symphony Hall (opened in 1900), the first building with scientifically formulated acoustics.

In the second half of the 20th century, the rising level of noise in the modern world — particularly in urban areas — prompted a whole new series of investigations, dealing in large part with the physiological and psychological effects of noise on humans.

This article was updated in conjunction with AI technology, then fact-checked and edited by a HowStuffWorks editor.

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Why isn’t there any sound in space? An astronomer explains why in space no one can hear you scream

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Curious Kids is a series for children of all ages. If you have a question you’d like an expert to answer, send it to [email protected] .

How far can sound travel through space, since it’s so empty? Is there an echo in space? – Jasmine, age 14, Everson, Washington

In space, no one can hear you scream.

You may have heard this saying. It’s the tagline from the famous 1979 science fiction movie “ Alien .” It’s a scary thought, but is it true? The simple answer is yes, no one can hear you scream in space because there is no sound or echo in space.

I’m a professor of astronomy , which means I study space and how it works. Space is silent – for the most part.

How sound works

To understand why there’s no sound in space, first consider how sound works. Sound is a wave of energy that moves through a solid, a liquid or a gas.

Sound is a compression wave . The energy created when your vocal cords vibrate slightly compresses the air in your throat, and the compressed energy travels outward.

A good analogy for sound is a Slinky toy . If you stretch out a Slinky and push hard on one end, a compression wave travels down the Slinky.

When you talk, your vocal cords vibrate. They jostle air molecules in your throat above your vocal cords, which in turn jostle or bump into their neighbors, causing a sound to come out of your mouth.

Sound moves through air the same way it moves through your throat. Air molecules near your mouth bump into their neighbors, which in turn bump into their neighbors, and the sound moves through the air. The sound wave travels quickly , about 760 miles per hour (1,223 kilometers per hour), which is faster than a commercial jet.

Space is a vacuum

So what about in space?

Space is a vacuum, which means it contains almost no matter. The word vacuum comes from the Latin word for empty .

Sound is carried by atoms and molecules. In space, with no atoms or molecules to carry a sound wave, there’s no sound. There’s nothing to get in sound’s way out in space, but there’s nothing to carry it, so it doesn’t travel at all. No sound also means no echo. An echo happens when a sound wave hits a hard, flat surface and bounces back in the direction it came from.

By the way, if you were caught in space outside your spacecraft with no spacesuit, the fact that no one could hear your cry for help is the least of your problems. Any air you still had in your lungs would expand because it was at higher pressure than the vacuum outside. Your lungs would rupture. In a mere 10 to 15 seconds , you’d be unconscious due to a lack of oxygen.

Sound in the solar system

Scientists have wondered how human voices would sound on our nearest neighboring planets, Venus and Mars. This experiment is hypothetical because Mars is usually below freezing , and its atmosphere is thin, unbreathable carbon dioxide . Venus is even worse – its air is hot enough to melt lead, with a thick carbon dioxide atmosphere.

On Mars, your voice would sound tinny and hollow, like the sound of a piccolo . On Venus , the pitch of your voice would be much deeper, like the sound of a booming bass guitar. The reason is the thickness of the atmosphere. On Mars the thin air creates a high-pitched sound, and on Venus the thick air creates a low-pitched sound. The team that worked this out simulated other solar system sounds , like a waterfall on Saturn’s moon Titan.

Deep space sounds

While space is a good enough vacuum that normal sound can’t travel through it, it’s actually not a perfect vacuum, and it does have some particles floating through it.

Beyond the Earth and its atmosphere, there are five particles in a typical cubic centimeter – the volume of a sugar cube – that are mostly hydrogen atoms. By contrast, the air you are breathing is 10 billion billion (10 19) times more dense. The density goes down with distance from the Sun, and in the space between stars there are 0.1 particles per cubic centimeter. In vast voids between galaxies , it is a million times lower still – fantastically empty.

The voids of space are kept very hot by radiation from stars. The very spread-out matter found there is in a physical state called a plasma .

A plasma is a gas in which electrons are separated from protons. In a plasma, the physics of sound waves get complicated . Waves travel much faster in this low-density medium, and their wavelength is much longer.

In 2022, NASA released a spectacular example of sound in space . It used X-ray data to make an audible recording that represents the way a massive black hole stirs up plasma in the Perseus galaxy cluster, 250 million light years from Earth. The black hole itself emits no sound, but the diffuse plasma around it carries very long wavelength sound waves.

The natural sound is far too low a frequency for the human ear to hear, 57 octaves below middle C, which is the middle note on a piano and in the middle of the range of sound people can hear. But after raising the frequency to the audible range, the result is chilling – it’s the sound of a black hole growling in deep space.

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Course: physics library   >   unit 8, production of sound.

• Sound Properties: Amplitude, period, frequency, wavelength
• Speed of Sound
• Relative speed of sound in solids, liquids, and gases
• Mach numbers
• Decibel Scale
• Why do sounds get softer?
• Ultrasound medical imaging

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Video transcript

• Sound Waves
• Speed Of Sound Propagation

Speed of Sound

A sound wave is fundamentally a pressure disturbance that propagates through a medium by particle interaction. In other words, sound waves move through a physical medium by alternately contracting and expanding the section of the medium in which it propagates. The rate at which the sound waves propagate through the medium is known as the speed of sound. In this article, you will discover the definition and factors affecting the speed of sound.

Speed of Sound Definition

The speed of sound is defined as the distance through which a sound wave’s point, such as a compression or a rarefaction, travels per unit of time. The speed of sound remains the same for all frequencies in a given medium under the same physical conditions.

Speed of Sound Formula

Since the speed of sound is the distance travelled by the sound wave in a given time, the speed of sound can be determined by the following formula:

v = λ f

Where v is the velocity, λ is the wavelength of the sound wave, and f is the frequency.

The relationship between the speed of sound, its frequency, and wavelength is the same as for all waves. The wavelength of a sound is the distance between adjacent compressions or rarefactions . The frequency is the same as the source’s and is the number of waves that pass a point per unit time.

Solved Example:

How long does it take for a sound wave of frequency 2 kHz and a wavelength of 35 cm to travel a distance of 1.5 km?

We know that the speed of sound is given by the formula:

v = λ ν

Substituting the values in the equation, we get

v = 0.35 m × 2000 Hz = 700 m/s

The time taken by the sound wave to travel a distance of 1.5 km can be calculated as follows:

Time = Distance Travelled/ Velocity

Time = 1500 m/ 700 m/s = 2.1 s

Factors Affecting the Speed of Sound

Density and temperature of the medium in which the sound wave travels affect the speed of sound.

Density of the Medium

When the medium is dense, the molecules in the medium are closely packed, which means that the sound travels faster. Therefore, the speed of sound increases as the density of the medium increases.

Temperature of the Medium

The speed of sound is directly proportional to the temperature. Therefore, as the temperature increases, the speed of sound increases.

Speed of Sound in Different Media

The speed of the sound depends on the density and the elasticity of the medium through which it travels. In general, sound travels faster in liquids than in gases and quicker in solids than in liquids. The greater the elasticity and the lower the density, the faster sound travels in a medium.

Speed of Sound in Solid

Sound is nothing more than a disturbance propagated by the collisions between the particles, one molecule hitting the next and so forth. Solids are significantly denser than liquids or gases, and this means that the molecules are closer to each other in solids than in liquids and liquids than in gases. This closeness due to density means that they can collide very quickly. Effectively it takes less time for a molecule of a solid to bump into its neighbouring molecule. Due to this advantage, the velocity of sound in a solid is faster than in a gas.

The speed of sound in solid is 6000 metres per second, while the speed of sound in steel is equal to 5100 metres per second. Another interesting fact about the speed of sound is that sound travels 35 times faster in diamonds than in the air.

Speed of Sound in Liquid

Speed of Sound in Water

The speed of sound in water is more than that of the air, and sound travels faster in water than in the air. The speed of sound in water is 1480 metres per second. It is also interesting that the speed may vary between 1450 to 1498 metres per second in distilled water. In contrast, seawater’s speed is 1531 metres per second when the temperature is between 20 o C to 25 o C.

Speed of Sound in Gas

We should remember that the speed of sound is independent of the density of the medium when it enters a liquid or solid. Since gases expand to fill the given space, density is relatively uniform irrespective of gas type, which isn’t the case with solids and liquids. The velocity of sound in gases is proportional to the square root of the absolute temperature (measured in Kelvin). Still, it is independent of the frequency of the sound wave or the pressure and the density of the medium. But none of the gases we find in real life is ideal gases , and this causes the properties to change slightly. The velocity of sound in air at 20 o C is 343.2 m/s which translates to 1,236 km/h.

Speed of Sound in Vacuum

The speed of sound in a vacuum is zero metres per second, as there are no particles present in the vacuum. The sound waves travel in a medium when there are particles for the propagation of these sound waves. Since the vacuum is an empty space, there is no propagation of sound waves.

Table of Speed of Sound in Various Mediums

Another very curious fact is that in solids, sound waves can be created either by compression or by tearing of the solid, also known as Shearing. Such waves exhibit different properties from each other and also travel at different speeds. This effect is seen clearly in Earthquakes. Earthquakes are created due to the movement of the earth’s plates, which then send these disturbances in the form of waves similar to sound waves through the earth and to the surface, causing an Earthquake. Typically compression waves travel faster than tearing waves, so Earthquakes always start with an up-and-down motion, followed after some time by a side-to-side motion. In seismic terms, the compression waves are called P-waves, and the tearing waves are called S-waves . They are the more destructive of the two, causing most of the damage in an earthquake.

Visualise sound waves like never before with the help of animations provided in the video

Frequently Asked Questions – FAQs

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June 27, 2019

What Do You Hear Underwater?

A submerged science activity from Science Buddies

By Science Buddies & Sabine De Brabandere

Make waves--underwater! Learn how sound travels differently in water than it does in the air. 

George Retseck

Key Concepts Physics Sound Waves Biology

Introduction Have you ever listened to noises underwater? Sound travels differently in the water than it does in the air. To learn more, try making your own underwater noises—and listening carefully. 

Background Sound is a wave created by vibrations. These vibrations create areas of more and less densely packed particles. So sound needs a medium to travel, such as air, water—or even solids. 

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Sound waves travel faster in denser substances because neighboring particles will more easily bump into one another. Take water, for example. There are about 800 times more particles in a bottle of water than there are in the same bottle filled with air. Thus sound waves travel much faster in water than they do in air. In freshwater at room temperature, for example, sound travels about 4.3 times faster than it does in air at the same temperature.

Sound traveling through air soon becomes less loud as you get farther from the source. This is because the waves’ energy quickly gets lost along the way. Sound keeps its energy longer when traveling through water because the particles can carry the sound waves better. In the ocean, for example, the sound of a humpback whale can travel thousands of miles!

Underwater sound waves reaching us at a faster pace and keeping their intensity longer seem like they should make us perceive those sounds as louder when we are also underwater. The human ear, however, evolved to hear sound in the air and is not as useful when submerged in water. Our head itself is full of tissues that contain water and can transmit sound waves when we are underwater. When this happens, the vibrations bypass the eardrum, the part of the ear that evolved to pick up sound waves in the air. 

Sound also interacts with boundaries between two different mediums, such as the surface of water. This boundary between water and air, for example, reflects almost all sounds back into the water. How will all these dynamics influence how we perceive underwater sounds? Try the activity to find out! 

Bathtub or swimming pool (a very large bucket can work, too)

Two stainless steel utensils (for example, spoons or tongs)

Two plastic utensils

Small ball 

Adult helper

An area that can get wet (if not performing the activity at a pool)

Floor cloth to cleanup spills (if not performing the activity at a pool)

Other materials to make underwater sounds (optional)

Access to a swimming pool (optional)

Internet access (optional)

Preparation

Fill the bathtub with lukewarm water—or head to the pool—and bring your helper and other materials.

Ask your helper to click one stainless steel utensil against another. Listen. How would you describe the sound? 

In a moment, your helper will click one utensil against the other underwater . Do you think you will hear the same sound? 

Ask your helper to click one utensil against the other underwater. Listen. Does the sound appear to be louder or softer? Is what you hear different in other ways, too?

Submerge one ear in the water. Ask your helper to click one utensil against the other underwater. Listen. How would you describe this sound? 

Ask your helper to click one utensil against the other underwater soon after you submerge your head. Take a deep breath, close your eyes and submerge your head completely or as much as you feel comfortable doing. Listen while you hold your breath underwater (come up for air when you need to!). Does the sound appear to be louder or softer? Does it appear to be different in other ways? 

Repeat this sequence but have your helper use two plastic utensils banging against each other instead.

Repeat the sequence again, but this time listen to a small ball being dropped into the water. Does the sound of a ball falling into the water change when you listen above or below water? Does your perception of this sound change? Why would this happen? 

Switch roles. Have your helper listen while you make the sounds. 

Discuss the findings you gathered. Do patterns appear? Can you conclude something about how humans perceive sounds when submerged in water? 

Extra : Test with more types of sounds: soft as well as loud sounds, high- as well as low-pitched sounds. Can you find more patterns?

Extra: To investigate what picks up the sound wave when you are submerged, use your fingers to close your ears or use earbuds when submerging your head. How does the sound change when you close off your ear canal underwater? Does the same happen when you close off your ear canal when you are above water? If not, why would this be different? 

Extra: Go to the swimming pool and listen to the sound of someone jumping into the water. Compare your perception of the sound when you are submerged with when your head is above the water. How does your perception change? Close your eyes. Can you tell where the person jumped into the water when submerged? Can you tell when you have your head above the water?

Extra: Research ocean sounds and how sounds caused by human activity impact aquatic animals.  

Observations and Results Was the sound softer when it was created underwater and you listened above the water? Did it sound muffled when you had only your ear submerged? Was it fuller when you had your head submerged? 

Sound travels faster in water compared with air because water particles are packed in more densely. Thus, the energy the sound waves carry is transported faster. This should make the sound appear louder. You probably perceived it as softer when you were not submerged, however, because the water surface is almost like a mirror for the sound you created. The sound most likely almost completely reflected back into the water as soon as it reached the surface. 

When you submerged only your ear, the sound probably still appeared muffled. This happens because the human ear is not good at picking up sound in water—after all, it evolved to pick up sound in air. 

When you submerged your head, the sound probably sounded fuller. That is because our head contains a lot of water, which allows the tissue to pick up underwater sound—without relying on the eardrum. It also explains why closing your ear canal makes almost no difference in the sound you pick up while you are underwater. 

If you tried to detect where the sound came from when submerged, you probably had a hard time. Our brain uses the difference in loudness and timing of the sound detected by each ear as a clue to infer where the sound came from. Because sound travels faster underwater and because you pick up sound with your entire head when you are submerged, your brain loses the cues that normally help you determine where the sound is coming from. 

More to Explore Discovery of Sound in the Sea , from the University of Rhode Island and the Inner Space Center Can You Hear Sounds in Outer Space? , from Science Buddies Talk through a String Telephone , from Scientific American Sound Localization , from Science Buddies  Ears: Do Their Design, Size and Shape Matter? , from Scientific American STEM Activities for Kids , from Science Buddies 

This activity brought to you in partnership with Science Buddies

Ukraine-Russia war latest: At least four dead in daytime missile strike on port city - as massive building on fire

It is likely to be a "very difficult summer" for Ukrainian forces in the face of increased Russian attacks, military analyst Sean Bell says. Listen to a Daily podcast on whether the UK should send troops to Ukraine as you scroll.

Monday 29 April 2024 22:48, UK

• At least four killed in daytime missile attack on Odesa
• Watch: Massive building in flames after attack
• Ukraine in for 'difficult summer' as Russia preparing 'major offensive'
• North Korea expresses 'concern' over US sending long-range missiles to Ukraine
• Explained : Why is Chasiv Yar the next target for Russia?
• Your questions answered: Will Ukraine launch another spring offensive?
• Big picture : What you need to know as a new week begins
• Listen to the Sky News Daily above and  tap here  to follow wherever you get your podcasts

As we reported a short time ago, the Duchess of Edinburgh has met with Volodymyr Zelenskyy in Ukraine, in what marks the first visit to the country by a member of the Royal Family since the war begin.

Sophie met the Ukrainian president and first lady Olena Zelenska and delivered a message to them on behalf of the King, Buckingham Palace said.

You can watch footage from her trip here...

Throughout the day, we've been reporting on a Russian attack on the city of Odesa in Ukraine, which has killed at least four people. 

These images show a burning educational institution building, which was struck. 

Airline Finnair has said it is pausing flights to Tartu in eastern Estonia for the next month, due to GPS disturbances in the area.

"Finnair will suspend its daily flights to Tartu, Estonia, from 29 April to 31 May, so that an alternative approach solution that does not require a GPS signal can be put in place at Tartu Airport," the Finnish airline said in a statement.

Finnair last week had to divert two flights back to Helsinki after GPS interference prevented the approach to Tartu airport, although a spokesperson said the company did not now where the interference came from.

However, Tallinn seems certain as where the issues are originating. 

"It is a fact that Russia affects GPS devices in our region’s airspace," Estonia's foreign minister said via a spokesperson.

Margus Tsahkna added that Estonia will raise the issue of GPS interference with its neighbours, and intends to discuss it with the EU and NATO. 

GPS jamming and spoofing have grown worse in eastern Europe, the Black Sea and the Middle East, all areas close to conflict zones, according to industry group OpsGroup. 

More than 30 Ukrainian conscripts have died while trying to cross the border illegally to avoid mobilisation, a Ukrainian official has said.

Andriy Demchenko, spokesman for the State Border Guard Service,  told Ukrinform that some men are prepared to pay "large sums" of money to groups promising to smuggle them across the border safely.

"Then they are faced with the fact that the route runs along a mountain river," he said.

Many conscripts have lost their lives after realising they didn't have the strength to swim the river, Mr Demchenko added.

"In total, since the beginning of the full-scale invasion, about 30 people have died trying to cross the border illegally," he said.

Such attempts occur "every day", he said.

For context: Ukraine has been under martial law since the Russian invasion in February 2022.

It lets draft officers call up men of a certain age to fight on the front line.

In April, Volodymyr Zelenskyy signed off a new law lowering the age of draft-eligible men from 27 to 25, in a bid to boost troop numbers in his depleted ranks.

The Duchess of Edinburgh has met with Volodymyr Zelenskyy in Ukraine, in what marks the first visit to the country by a member of the Royal Family since the war begin.

Her visit is aimed at demonstrating "solidarity with the women, men and children impacted by the war and in a continuation of her work to champion survivors of conflict-related sexual violence", the palace said.

Three women and a man have died after a Russian attack on Odesa.

A further 28 people have been injured, including two children aged five and 16. A pregnant woman has also been hurt.

This video shows the aftermath of the attack. 

Debris recovered from a missile that landed in the Ukrainian region of Kharkiv on 2 January was North Korean, the Reuters news agency is reporting.

Citing a United Nations sanctions monitor, Reuters said debris recovered was from a Hwasong-11 series ballistic missile - made in North Korea.

Three sanctions monitors travelled to Ukraine earlier this month to inspect the debris - and found no evidence that the missile was made by Russia. 

They "could not independently identify from where the missile was launched, nor by whom". 

"Information on the trajectory provided by Ukrainian authorities indicates it was launched within the territory of the Russian Federation," they wrote in an April 25 report to the UN Security Council's North Korea sanctions committee. 

"Such a location, if the missile was under control of Russian forces, would probably indicate procurement by nationals of the Russian Federation," they said, adding that this would be a violation of the arms embargo imposed on North Korea in 2006. 

International leaders have long accused North Korea of supplying Russia with weapons.

Both Moscow and Pyongyang have denied the accusations, but vowed last year to deepen military relations. 

The situation in Odesa is fast-moving after the city in southern Ukraine came under Russian missile attack this afternoon.

Three women and a man have died, bringing the total number of people killed to four, according to regional governor Oleg Kiper.

He said a further 28 people have been injured, including two children aged five and 16. A pregnant woman has also been hurt.

Four people are "fighting for their lives," he said in a Telegram post .

A big building housing part of the Odessa Law Academy is ablaze after the strike...

The number of people injured in Russia's missile attack on Odesa has increased.

Regional governor Oleg Kiper said he was aware of 17 injured people, of whom at least two are in a "serious condition". Separately, Odesa mayor Gennadiy Trukhanov said at least 20 people were hurt.

Emergency services continue to work at the scene, Mr Kiper said. Earlier, he reported that at least two people had been killed in the attack (see 17.46 post).

The Odesa region has been repeatedly targeted by Russia during the war.

Last month, a Russian ballistic missile attack on a residential area killed at least 20 people and wounded more than 70.

Ukrainian troops are still defending their positions on the frontline while grappling with depleted weapons supplies and increased Russian attacks.

Western support is on full display in the pictures below, with soldiers of the Ukrainian army's 25th separate airborne brigade operating a German-made Marder infantry fighting vehicle.

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