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What, really, is the speed of sound?

Unlike the speed of light, this one isn't constant.

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We know that the speed of light seems to be the upper limit for how fast something can travel in the universe. But there’s a much lower speed limit that we’ve only recently (in the grand scheme of things) managed to overcome here on Earth: the speed of sound.

You’ve heard the term before, and you might even know its exact value or, more accurately, values.

But why exactly does sound have a ‘speed’? Is it the same everywhere? And what happens if you go over the limit? Well, one thing is for sure — sound won’t give you a fine for it. It will cause a mighty boom to mark the occasion, though, because going over the speed of sound isn’t an easy thing to pull off.

In Earth’s atmosphere, sound can travel at around 345 meters per second. Let’s take a look at why this limit exists, what says it should be this way, and just why things go boom when you blast through it. But first, let’s start at with the basics:

What is a sound wave

What we perceive as sound is actually motion. Sound is, fundamentally, a movement or vibration of particles, most commonly those in the atmosphere, where we do most of our talking and sound-making.

In very broad lines, any object in motion will come into contact with the particles in their environment. Let’s take talking as an example. When someone speaks, their lungs collide with and push out air that their vocal cords modulate to create certain sounds. This will push the air in their immediate vicinity, which will make its molecules collide with air molecules farther away, and so on, until the motion reaches the air particles next to you. They will then collide with your eardrums, which ‘translates’ it into the sensation of sound.

Two ways to represent the physics of sound. Areas with more dots (corresponding to peaks) show high air pressure, while whiter areas (corresponding to throughs) show areas of low pressure that interact to create sound. This pressure is generated by moving air.
Image via Wikimedia.

So from a physical point of view, sound behaves quite like waves do on a beach. Its volume is directed by how high the wave goes (amplitude) and its pitch is formed by how often these waves hit the shore (frequency). The farther a wave travels, the less energy it has (so the less pressure it can exert on new particles), which is why eventually sound dies out and we can’t hear something halfway around the world. More on sounds here.

The speed of sound is essentially the speed that these ‘acoustic waves’ can travel at through a substance. Leading us neatly to the role these substances (called “the medium”) play here.

Not all things are equal

The source of sound only plays a limited part in its propagation. Sound propagation is almost entirely dependent on the medium.

First off, this means that sound can’t propagate through void, as there is nothing to carry it. One handy example is that in space, nobody can hear you scream; but if you place your visor on another’s astronaut’s visor, they will. Secondly, a medium can’t carry sound unless it has some elasticity, although this is more of an academic point as every material is elastic to some degree. The corollary of this is that the more elastic our medium, the faster sound will travel through it.

Elasticity is the product of two traits: the ability to resist deformation (its ‘elastic modulus’ or rigidity) and how much you can alter it before it stops coming back to its original shape (its ‘elastic limit’ or flexibility). Steel and rubber are both very elastic, but the former is rigid while the later is flexible.

Density has a bit of a more complicated relationship to the speed of sound. Density is basically a measure of how much matter there is in a given space. On the one hand closely-packed, lightweight particles allow for higher speeds of sound as there’s less empty space they need to travel over to hit their neighbors. But if these particles are heavy and more spread apart, they will slow the sound down (as big, heavy particles are harder to move). Sound will also attenuate faster through this last type of material. In general, elastic properties tend to have more of an impact on the speed of sound than density.

A basic example involves hydrogen, oxygen, and iron. Hydrogen and oxygen have nearly the same elastic properties, but hydrogen is much less dense than oxygen. The speed of sound through hydrogen is 1,270 meters per second, but only 326 m/s through oxygen. Iron, although much denser than either of them, is also much more elastic. Sound traveling through an iron bar can reach up to 5,120 m/s.

One other thing to note here is that fluids only carry sound as compression waves (particles bumping into each other in the direction the wave is propagating. Solids carry it both as compression and shear waves (perpendicular to the direction of propagation). This is due to the fact that you can’t cut fluids with a knife (they have a shear modulus of 0). A fluid’s molecules can move too freely from one another for such motions to create such waves.

Sonic boom

So far we’ve seen that sound has a maximum speed it can travel at, based on which material it is propagating through. By ‘travelling’, we mean particles bumping into their neighbors creating wave-like areas of pressure.

So what happens when something moves faster than the speed these particles can reach? Well, you get a sonic boom, of course.

Slow-motion footage of a bullet traveling through ballistic gel. Notice how the gel in the middle is pushed away by the bullet before its edges and corners have time to move. The process is very similar to how airplanes form sonic booms. You can see the metal table buckling under the pressure.
Image via YouTube.

Despite the name, sonic booms are more like sonic yelling. When an object is moving faster than sound can travel in its environment, it generates a thunder-like sound. Depending on how far away the source is, this boom is strong enough to damage structures and break windows.

An airplane moving faster than the speed of sound will compress the air in front of it, as this air can only move at the speed of sound. It can’t physically get out of the way fast enough. Eventually, all this compressed, moving air (which is, in essence, sound) is blasted away from the aircraft’s nose at Mach 1 (the speed of sound through air). If anyone is close enough to be reached by this blast of ultra-pressurized air, they hear the sonic boom.

Although it is perceived as an extremely loud burst of sound by a static observer, the sonic boom is a continuous phenomenon. As long as an object moves faster than sound, it will keep creating this area of ultra-compressed air, and leave a continuous boom in its wake. One nifty fact about sonic booms is that you can’t hear them coming — they move faster than sound, so you can only hear them after they’ve passed you.

Humans have only recently gone above the speed of sound, with the first supersonic flight recorded in 1947. Since then, such flights have been banned above dry land in the US and EU, in order to protect people and property (although they can still be carried out with proper authorization). Faster-than-sound travel, however, is still an alluring goal. One way to allow for supersonic speeds without blasting all the windows in the neighborhood is to travel through a vacuum or low-pressure air — a cornerstone idea of the Hyperloop.

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