# 10.2 Shock waves and sonic booms

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## Shock waves and sonic booms

Now we know that the waves move away from the source at the speed of sound. What happens if the source moves at the same time as emitting sounds? Once a sound wave has been emitted it is no longer connected to the source so if the source moves it doesn't change the way the sound wave is propagating through the medium. This means a source can actually catch up to the sound waves it has emitted.

The speed of sound is very fast in air, about $340\phantom{\rule{4pt}{0ex}}{\mathrm{m}·\mathrm{s}}^{-1}$ , so if we want to talk about a source catching up to sound waves then the source has to be able to move very fast. A good source of sound waves to discuss is a jet aircraft. Fighter jets can move very fast and they are very noisy so they are a good source of sound for our discussion. Here are the speeds for a selection of aircraft that can fly faster than the speed of sound.

 Aircraft speed at altitude ( ${\mathrm{km}·\mathrm{h}}^{-1}$ ) speed at altitude ( ${\mathrm{m}·\mathrm{s}}^{-1}$ ) Concorde 2 330 647 Gripen 2 410 669 Mirage F1 2 573 715 Mig 27 1 885 524 F 15 2 660 739 F 16 2 414 671

## Subsonic flight

Subsonic

Subsonic refers to speeds slower than the speed of sound.

When a source emits sound waves and is moving slower than the speed of sound you get the situation in this picture. Notice that the source moving means that the wavefronts, and therefore peaks in the wave, are actually closer together in the one direction and further apart in the other.

If you measure the waves on the side where the peaks are closer together you'll measure a different wavelength than on the other side of the source. This means that the noise from the source will sound different on the different sides. This is called the Doppler Effect .

Doppler Effect

when the wavelength and frequency measured by an observer are different to those emitted by the source due to movement of the source or observer.

## Supersonic flight

Supersonic

Supersonic refers to speeds faster than the speed of sound.

If a plane flies at exactly the speed of sound then the waves that it emits in the direction it is flying won't be able to get away from the plane. It also means that the next sound wave emitted will be exactly on top of the previous one, look at this picture to see what the wavefronts would look like:

Sometimes we use the speed of sound as a reference to describe the speed of the object (aircraft in our discussion).

Mach Number

The Mach Number is the ratio of the speed of an object to the speed of sound in the surrounding medium.

Mach number is tells you how many times faster than sound the aircraft is moving.

• Mach Number $<$ 1 : aircraft moving slower than the speed of sound
• Mach Number $=$ 1 : aircraft moving at the speed of sound
• Mach Number $>$ 1 : aircraft moving faster than the speed of sound

To work out the Mach Number divide the speed of the aircraft by the speed of sound.

$\mathrm{Mach}\phantom{\rule{4pt}{0ex}}\mathrm{Number}=\frac{{\mathrm{v}}_{\mathrm{aircraft}}}{{\mathrm{v}}_{\mathrm{sound}}}$

Remember: the units must be the same before you divide.

If the aircraft is moving faster than the speed of sound then the wavefronts look like this:

If the source moves faster than the speed of sound, a cone of wave fronts is created. This is called a Mach cone. From constructive interference, we know that two peaks that add together form a larger peak. In a Mach cone many, many peaks add together to form a very large peak. This is a sound wave so the large peak is a very, very loud sound wave. This sounds like a huge "boom" and we call the noise a sonic boom .

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