# 18.13 Sound

When an object moves in air, it must push the air away from it; it changes the motion of the air and, by definition, so exerts a force on it (post 16.13). Since pressure is simply force divided by the area on which it acts (post 17.5), the object increases the pressure in the direction in which it is moving. However, the pressure behind it drops, because there is less air (it’s like letting some air out of a balloon or a tyre).

Now let’s think about what happens to the air around a vibrating string, like those in post 18.12.

When the string moves upwards, it produces a band of high-pressure air above it and leaves a band of low-pressure air behind it.

When the string moves downwards, it produces a band of high-pressure air below it and leaves a band of low-pressure air above it.

As the string continues to vibrate is produces more bands of high and low-pressure air; these bands are produced at the same frequency as the string vibrates and move upwards and downwards away from the string. This is shown in the picture above, where the grey bars represent high-pressure air and the white bars low-pressure air. An animation is shown at: https://www.youtube.com/watch?v=aPswnDcteS4.

If we plot the pressure along the direction of propagation at a fixed time, we get a graph that looks something like the picture above.

If we look at a fixed point along the direction of propagation and plot the pressure at this point against time, we get a graph that looks something like the picture below.

These graphs show that the vibrating string is producing a pressure wave in the air (see post 18.10).

However, the air in this pressure wave does not behave like water in the water waves of post 18.10. In a water wave, the water oscillates perpendicular to the direction of propagation. In our pressure wave, the air oscillates in the direction of propagation. The water wave was an example of a transverse wave (post 18.10); the pressure wave is an example of a longitudinal wave.

When the pressure wave meets your ear it makes a membrane, called the tympanic membrane, oscillate. These oscillations are amplified by a system of bone levers, called the malleus, incus and stapes. The amplified vibrations are transmitted to the cochlea. The cochlea contains specialised cells, called hair cells, which have hair-like protuberances. When a vibration has the same frequency as the natural frequency (post 18.8) of vibration of a “hair”, the hair vibrates and changes the cell membrane so that potassium ions (post 16.39) move across it. This changes the electrical potential (post 17.44) inside the cell which is transmitted to a nerve and on to the brain. You call the sensation produced in your brain sound.

So we call pressure waves in the air sound waves.

Different hair cells have hairs of different lengths and so have different natural frequencies (post 18.8). Your brain can detect which cells are transmitting a signal and so can distinguish different frequencies of vibration. You call the difference in sensation caused by the different frequencies pitch – a high pitch corresponds to a high frequency.

Bats use very high frequency air pressure waves for navigation. Their frequency is too high to be detected by our hair cells, so we call these waves ultrasound. Ultrasound is also used to form images of the inside of the human body – for examining the motion of heart valves and for looking at babies before they are born.

Sound waves can also produce mechanical vibrations in a device called a microphone. The microphone produces an electrical current (post 17.44) that oscillates with the same frequency as the sound. This electrical signal can be amplified and recorded or transmitted to a loudspeaker. The loudspeaker turns the electrical current into a mechanical vibration with the same frequency. This mechanical vibration produces a sound wave in the surrounding air.

In conclusion, sound is a pressure wave in the air that is produced by, and can cause, mechanical vibrations. Detecting these sound waves involves converting mechanical energy (post 16.21) into electrical energy (post 17.45). Reproducing sound involves converting an electrical signal into a mechanical vibration that produces a sound wave. The previous sentence doesn’t apply only to devices like amplifiers and loudspeakers. If you want to produce a sound your brain sends an electrical signal, through your nervous system, that makes you vibrate flaps of membrane (“vocal cords”) in your larynx.

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