Sound

Sound is produced by something vibrating

Every sound begins with a vibrating source. Strike a tuning fork and you can see the prongs swinging backwards and forwards; hold the prongs against a table and the note suddenly becomes louder, because the vibration has been passed into the wood. Pluck a guitar string, hit a drum skin or speak, and the same thing is happening: a source is oscillating backwards and forwards, and that vibration travels away through the air as a sound wave.

The vibration pushes and pulls on the particles of the air next to the source, and those particles push and pull on their neighbours, so the disturbance is handed on from particle to particle. This is why sound needs a medium: there must be particles present to pass the vibration along. Put a ringing electric bell inside a jar and pump the air out, and the sound fades away to nothing even though the hammer is still moving. In a vacuum there are no particles, so there is nothing to carry the vibration and no sound travels at all.

This is the key difference between sound and light. Light is an electromagnetic wave and travels happily through a vacuum, which is why you can see the Sun but cannot hear it exploding. Sound is a mechanical wave and always needs a material - a solid, a liquid or a gas - to travel through.

Sound is a longitudinal wave: compressions and rarefactions

Sound is a longitudinal wave. The particles of the medium vibrate backwards and forwards along the same line as the wave travels, not up and down across it. Picture a row of people standing in a line, each giving the person in front a gentle shove: every person moves only a little forwards and back, but the shove travels all the way down the line. That is exactly what the air particles do.

Where the particles are pushed closer together the air is squashed, and this region is called a compression. Where they are pulled further apart the air is stretched, and this region is called a rarefaction. Compressions and rarefactions follow one another along the wave, and the distance from one compression to the next is the wavelength of the sound.

The particles themselves do not travel from the source to your ear. Each particle vibrates only a tiny distance about a fixed point and then passes the vibration on to its neighbour. What actually travels is the energy and the pattern of compressions and rarefactions, not the air. That is why you can smell a bonfire long before you hear it: the hot gases drift towards you slowly, while the sound arrives almost instantly.

Because sound is longitudinal it can travel through solids, liquids and gases, because in all of them the particles can be pushed together and pulled apart. A transverse wave such as a wave on a rope or light cannot be passed through a gas in this way.

• Longitudinal wave: the particles vibrate along the direction in which the wave travels.
• Compression: a region where the particles are closer together than normal, so the pressure is higher.
• Rarefaction: a region where the particles are further apart than normal, so the pressure is lower.
• The particles vibrate about fixed positions, so it is the energy that moves along the wave, not the medium.

The speed of sound in different media

The speed of sound depends on the medium it is travelling through. In general, sound travels fastest in solids, more slowly in liquids and slowest in gases. The reason is the spacing of the particles and the forces between them: in a solid the particles are packed close together and held by strong forces, so a vibration is handed on from one particle to the next very quickly. In a gas the particles are far apart and only weakly interacting, so the disturbance takes much longer to pass along.

In air at room temperature the speed of sound is about 330 to 350 m/s, and a value of 340 m/s is normally used in calculations. The speed rises a little as the air gets warmer, because the particles move faster and pass the vibration on more quickly, so sound travels slightly faster on a hot day than on a cold one. The speed does not depend on how loud the sound is.

This is why you can hear an approaching train through the rails before you hear it through the air, and why a swimmer with their head underwater hears a splash on the poolside far more clearly than they would with their head above the water. The closer and more strongly held the particles are, the better the medium is at carrying the vibration.

Measuring the speed of sound in air

To find the speed of sound you need a distance and a time, and then you use speed = distance / time. Any method works provided you can measure how far the sound travels and how long it takes to get there.

Direct method with two people. Two students stand a measured distance apart in the open, say 100 m. One fires a starting pistol or bangs two blocks of wood together. The other starts a stopwatch when they see the flash (light arrives effectively instantly) and stops it when they hear the bang. Then speed of sound = distance / time. Repeating the measurement several times and taking an average reduces the random error, and using a longer distance makes the time larger, so the timing error matters less.

Echo method. Stand a measured distance from a large flat wall, for example 85 m. Clap your hands sharply and listen for the echo. Adjust the rate of clapping until each clap coincides with the echo of the previous clap, so that the time between claps is exactly the time for the sound to travel to the wall and back. The sound covers twice the distance to the wall, so speed of sound = (2 x distance to wall) / time. A hand-operated stopwatch has a large uncertainty here, so an electronic timer or data logger that measures the interval between claps is much more reliable.

The same experiment can be done with two microphones connected to a data logger placed a measured distance apart: the logger measures the small time delay between the two signals arriving, and speed = distance / time again. Notice that in every echo method the sound covers the distance to the reflector twice, and forgetting that factor of two is the commonest mistake in the whole topic.

Loudness and pitch: what amplitude and frequency do

Loudness depends on the amplitude of the wave, which is how far the particles are displaced from their rest position. A larger amplitude means bigger pressure changes in the compressions and rarefactions, and your ear detects that as a louder sound. Making a sound louder does not change its pitch at all.

Pitch depends on the frequency of the wave, which is the number of complete vibrations per second, measured in hertz (Hz). A high frequency means many compressions and rarefactions reach your ear every second, and you hear a high note. The frequency is fixed by the source, so it does not change as the sound spreads out, although the sound does get quieter because the same energy is spread over a larger area.

An oscilloscope trace shows the two properties separately. The height of the trace from the centre line shows the amplitude, so it tells you the loudness. The horizontal distance between one crest and the next shows the period, so it tells you the frequency, using frequency = 1 / period. A trace that is tall and has its crests close together is a loud, high-pitched sound; a short trace with its crests far apart is a quiet, low-pitched sound.

The human ear can detect only a limited range. Normal hearing covers about 20 Hz to 20 000 Hz (20 kHz). Sound below 20 Hz is called infrasound and sound above 20 kHz is called ultrasound; both are ordinary sound waves, but the human ear cannot hear them. The upper limit falls as you get older, which is why a very high-pitched whistle that a child hears easily may be completely silent to an adult.

Echoes: sound reflected from a surface

An echo is a sound wave that has been reflected from a surface and arrives back at your ear after the original sound. Sound reflects in the same way as light: it bounces off hard, flat, smooth surfaces such as a cliff face, a large wall, the side of a building or the sea bed. Soft, rough surfaces such as curtains, carpets and clothing absorb the sound instead, which is why a room full of soft furnishings sounds quieter than an empty one.

You only hear an echo as separate from the original sound if there is a gap of about 0.1 s or more between them, because the ear keeps hearing a sound for roughly that long after it stops. In 0.1 s sound travels about 34 m at 340 m/s, so the round trip must be more than about 34 m and the reflecting surface must be at least about 17 m away. Any closer and the reflected sound merges with the original, which is why you hear no echo in a small room but a clear one in a large hall or across a valley.

Echoes are useful as well as irritating. Sonar sends a pulse of sound down through water and times the echo from the sea bed, a wreck or a shoal of fish to find the depth or the distance. Bats hunt in the dark in exactly the same way, and a doctor uses ultrasound echoes to see inside the body.

Because the sound travels out to the reflector and back again, the total distance is twice the distance to the reflector, so distance to the reflector = (speed of sound x time) / 2. This single relationship is behind every echo, sonar and depth calculation you will meet.

Ultrasound and its uses

Ultrasound is sound with a frequency higher than 20 kHz, above the upper limit of human hearing. It is produced and detected electronically, which makes it easy to send out a very short pulse, wait for the echo and measure the time accurately.

Non-destructive testing (NDT). A pulse of ultrasound is sent into a metal casting, a weld or an aircraft wing. Wherever the sound meets a boundary - the far side of the metal, or a crack, void or bubble inside it - some of the sound is reflected back. The time taken for the echo to return gives the distance to the flaw using distance = (speed x time) / 2. The great advantage is that the material is not cut open or damaged, so every component can be checked.

Medical scanning of soft tissue. A probe held against the skin sends pulses of ultrasound into the body and detects the echoes from the boundaries between tissues of different density, for example between muscle and bone or between a fluid and a tissue. A computer builds these echoes into an image of the inside of the body. Ultrasound is used for scanning soft tissue such as the heart, the kidneys and an unborn baby because it does not use ionising radiation, so it is much safer than X-rays for repeated use and for a developing foetus.

Sonar. A ship or a fishing boat sends an ultrasound pulse downwards and measures the time until the echo returns from the sea bed or a shoal of fish. The depth is depth = (speed of sound in water x time) / 2, using a speed of about 1500 m/s in water. The same method, called echo sounding, is used to map the ocean floor.

All three uses follow the same pattern: send out a pulse, time the echo, and divide by two because the sound has travelled out and back.

• Non-destructive testing: find cracks and flaws inside metal without cutting it open.
• Medical scanning: image soft tissue from the echoes at boundaries between tissues of different density, with no ionising radiation.
• Sonar and echo sounding: find depth or distance from the time for a pulse to travel down and back through water.