Shockwave reflection

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The latest episode of Mythbusters features a myth with a deep physical explanation… no pun intended! Well, maybe. Anyway, the myth is that by diving under the water, you can escape injury from an explosion occurring above the surface. Adam and Jamie tried to solve this puzzle by experiment (what else), and their results seemed to show that the myth might actually be true, but I want to look at it from the theoretical standpoint: why might being underwater protect you from an explosion?

There is actually a not-too-obscure answer to this puzzle, and it has to do with refraction and reflection. These are phenomena that occur when a wave (of any sort — light, sound, or whatever) crosses a boundary between two media in which it has different speeds. Part of the wave bounces back (that’s reflection) and part of it continues through, but in a different direction (that’s refraction). Exactly how much of the wave’s power is reflected and how much is transmitted through, as well as the new direction of the transmitted part, depends on the angle of the incoming wave with respect to the surface, and also on the relative speed of the wave in the two materials.

Reflection and refraction of waves
Reflection and refraction of waves

Reflection and refraction are most often discussed in connection with light. Lenses, for example, work by refracting incoming light, since light travels slower in glass (or plastic) than in air. Because the surface of the lens is curved, it bends different light rays in different locations by different amounts, and this can be used to focus an image. But the same thing happens with pressure waves, like sound waves and explosive shockwaves, at the surface of a lake, because pressure waves travel faster in water than they do in air. It stands to reason, then, that part of the energy in a blast wave would be reflected off the surface of the lake, reducing the energy available to damage anyone (or anything) below the water.

Unfortunately, calculating how much energy is reflected and how much is transmitted when a shock wave hits water turns out to be a very involved problem, not something that can be learned and solved in a week ;-) Still, there are some qualitative things I can say about the process. Consider what happens to a pressure wave in air when it hits a boundary, such as a wall: the wall will vibrate a bit, but the wave mostly just bounces back. You’d expect that a similar sort of thing would happen if the wave hits a water surface instead, since compared to air, water is very “hard” — technically speaking, it has a very low compressibility. This is related to a material property called the bulk modulus, which basically measures how much the material resists being squashed (compressed). The bulk modulus of water is about 10000 times larger than that of air, so the increase in pressure applied by a wave will have a relatively minor effect on the water. It’ll have a much greater effect on the surrounding air, which means that that’s where most of the energy goes: back into the air.

If pressure waves don’t affect water that much, though, why was there such a huge splash every time the Mythbusters set off one of their explosions? The amount of energy in an explosion shockwave is so large that even “relatively minor” can be enough to throw a lot of water around! Since air is transparent, most of the wave’s effect on the air goes unnoticed.