Sound waves

Waves carry energy, not matter

A wave is a disturbance that carries energy from one place to another without any overall movement of matter. The particles of the material (the medium) wobble back and forth around the same spot and pass the energy on to their neighbours.

Waves that need a medium are called mechanical waves. Sound, water waves, waves on a rope and earthquake waves are all mechanical. Light is different: it can cross empty space (6C). Mechanical waves come in two types.

• Transverse waves: particles vibrate at right angles to the direction the wave travels, like a wave flicked along a rope.
• Longitudinal waves: particles vibrate back and forth along the direction the wave travels, like a push sent along a stretched slinky.

Sound is a longitudinal wave

Every sound starts with something vibrating: a guitar string, your vocal cords, a speaker cone. As the cone moves forward it squashes the air in front of it into a compression, where the particles are closer together and the pressure is a little higher. As it moves back it leaves a rarefaction, where particles are spread out and the pressure is a little lower. A stream of compressions and rarefactions spreads outwards: that is a sound wave.

Every wave can be described by a few measurements.

• Wavelength (λ, the Greek letter lambda): the distance from one compression to the next (or one crest to the next), in metres.
• Frequency (f): how many waves pass a point each second, in hertz (Hz). 1 Hz = 1 wave per second.
• Period (T): the time for one complete wave. T = 1 ÷ f.
• Amplitude: how far the particles move from their rest position. Bigger amplitude means more energy.

Wave speed, frequency and wavelength are linked by the wave equation:

wave speed (m/s) = frequency (Hz) × wavelength (m)
v = f λ

The speed of a wave is set by the medium it travels through. Changing the frequency doesn't make sound go faster; it makes the wavelength shorter so that v = f λ still holds.

The speed of sound

Sound is generally fastest in solids and slowest in gases, because the particles in a solid are tightly linked and pass on a push quickly. In air, sound travels faster when the air is warmer: roughly 331 + 0.6 × temperature (°C) m/s, because warmer particles move faster. In a vacuum there are no particles to vibrate, so space is silent. Astronauts talk by radio, which is an electromagnetic wave.

Pitch and loudness

A microphone and oscilloscope turn a sound into a graph of pressure against time.

• Pitch depends on frequency. A high-frequency wave sounds high; a low-frequency wave sounds low. Shorter, tighter or thinner strings vibrate faster and give higher notes.
• Loudness depends on amplitude. Plucking a string harder makes it vibrate further, not faster, so the note is louder but has the same pitch.

Young people can hear from about 20 Hz to 20 000 Hz. The top of the range falls with age and with noise damage. Sound below 20 Hz is infrasound (elephants and blue whales use it to call over long distances). Sound above 20 000 Hz is ultrasound (bats and dolphins use it to echolocate).

Loudness is measured in decibels (dB). The scale goes up in multiples: every extra 10 dB means ten times as much sound energy. A quiet library is about 40 dB, normal talking 60 dB, a lawnmower 90 dB, a rock concert 110 dB, and 120 dB or more is painful. Sounds above about 85 dB can permanently damage the tiny hair cells in your inner ear, and every extra 3 dB halves how long you can listen safely. Earbuds turned up to full volume on a train can easily pass 100 dB. Hearing loss from noise can't be reversed, so turn it down and take breaks.

Echoes, ultrasound and sonar

Sound reflects off hard surfaces, producing an echo. If you know the speed of sound and time how long an echo takes to return, you can work out the distance. Remember the sound has to go there and back.

distance = speed × time ÷ 2

• Sonar (sound navigation and ranging) maps the sea floor, finds schools of fish and detects submarines. Modern ships use a fan of beams to map a wide strip of sea floor at once. During the search for flight MH370, Australian-led teams mapped hundreds of thousands of square kilometres of the deep Indian Ocean floor that had never been surveyed in detail.
• Medical ultrasound sends pulses of 2 to 15 million Hz into the body. Echoes from the boundaries between tissues build up an image of an unborn baby, the heart or other organs. Unlike X-rays it is not ionising, so it is safe for pregnancy scans.
• Echolocation: microbats and dolphins send out clicks and listen to the echoes to find prey in darkness or murky water.

The yidaki

The yidaki (often called the didgeridoo) comes from the Yolŋu peoples of north-east Arnhem Land, and related instruments are played across northern Australia. It is made from a eucalyptus trunk or branch that termites have hollowed out. The player's lips buzz at the mouthpiece, and the column of air inside the tube vibrates at its natural frequency, which is set by the tube's length. A typical instrument about 1.3 m long gives a deep drone of around 65 to 80 Hz, close to the bottom of human hearing. Skilled players use circular breathing (breathing in through the nose while pushing air out from the cheeks) to keep the sound going without a break, and change the shape of their mouth and voice to add higher overtones and animal calls. Yolŋu makers select and test trees by tapping and listening, the same physics of resonance that instrument makers everywhere rely on.