Breaking the sound barrier

Like seen in the previous post [1], when an explosion is faster than the speed of sound, a shockwave is created, with a sonic boom. I didn’t detailed this phenomenon, then. So I will do it now by explaining what happens when an object producing sound moves becomes supersonic.

Properties of sound

A sound is a mechanical wave moving through a medium [2]. It is characterised as a sinusoid with an intensity and a period.

A static source creating sound emits this sinusoid in every direction in a shape similar to ripples on a water surface but in three dimension. In the following figure, the circles represent the peaks of the sinusoid.

The speed of sound isn’t absolute but relative to the medium it is in and is referred as Mach 1. The velocity will therefore be different when the sound travels in water than when it travels in air. In the air, at 15 °C (59 °F) and 0% humidity, the speed of sound is equal to 340.3 metres per second (1,116.5 ft/s).

Doppler effect

However, a sound source isn’t always static. When an object is moving, the wave will propagate from the new position, as illustrated in the following figure.

We can distinguish two noticeable parts in this figure.

First, on the left, the distance between the same point of two circles is greater than in the static source. Transposed as a sinusoid, it results in a curve with a greater period, so a lower frequency. Lower frequency means deeper tone. That is why an object moving from us sounds deeper than it should.

Then, on the right, the distance between the same point of two circles is lesser than in the static source. Transposed as a sinusoid, it results in a curve with a lesser period, so a higher frequency. Higher frequency means higher tone. That is why an object moving from us sounds higher than it should.

The Doppler effect is the characterisation of the change of frequency between an observer (us or a measure equipment) and a wave source moving relatively. This effect is the same if it is either the observer or the wave source which is moving. It is what happens when an ambulance passes next to you.

Mach 1 and more

The number of Mach is calculated with the following equation:

Mach 1 is equivalent to the speed of sound. When an object reaches Mach 1, it breaks the sound barrier, creating a sonic boom, and we obtain a wave front like in the next figure:

This wave front is the shockwave. When the speed of the object increases again, it becomes supersonic and the wave propagation keeps being delayed behind the object:

The shockwave angle we observe is equal to 1/Ma, the inverse of the number of Mach. We are able to the see with our naked eye the cone shape of the shockwave.

Last thing to point out, the sonic boom is not just when the object reaches Mach 1 and propagates from the point it reached it. In fact, it is hearable all along the edge of cone-shaped shockwave.

Fast objects

There are some objects that are able to go fast enough to reach the speed of sound and break the sound barrier. We will have an overview of a few of them.

The first that comes in my mind when I think about very fast object is a supersonic plane. Those military aircrafts can go up to Mach 3 [3]. In a very similar way, space shuttles can also be supersonic.

Bullets, at muzzle velocity (the speed when it leaves the end of the gun’s barrel), can reach 370 m/s and so be faster than the speed of sound (340.3 m/s). It results in sonic boom in addition to the sound of the gunfire itself.

Another object, more common, can also be supersonic, and this one might surprise you. I am talking about a whip, and more specifically, a bullwhip. When thrown, the end of the tail will exceed the speed of sound and create a small sonic boom.

Even though it is fun to imagine Indiana Jones breaking the sound barrier or amazing to watch an aircraft reach Mach 1, sonic boom and shock waves can be dangerous to the eardrum or to buildings when produced by massive objects.

References

[Sound wave propagation figures] Ejs Open Source 1 Dimension Doppler Effect Sound Wave Java Applet | Open Source Physics @ Singapore, https://weelookang.blogspot.com/2011/09/ejs-open-source-1-dimension-doppler.html

[1] All You Need Is Science, What triggers an explosion?

[2] All You Need Is Science, A B Sinusoid D E F G 🎶 (part 1)

[3] NASA Armstrong Fact Sheet: Sonic Booms | NASA, https://www.nasa.gov/centers/armstrong/news/FactSheets/FS-016-DFRC.html