Breaking the Sound Barrier
Date: 10/21/97 at 23:40:51 From: Gabrielle Mills Subject: Breaking Sound Barrier This is not really a math question, but I am a teacher and I am trying to find a way to incorporate breaking the sound barrier into a math lesson for my third grade class. Do you have any suggestions?
Date: 10/22/97 at 14:24:49 From: Doctor Tom Subject: Re: Breaking Sound Barrier Well, it might be more of a physics lesson, but that's okay - there's certainly some math involved. To break the sound barrier, you basically have to go faster than sound does in the fluid you're moving through (usually, of course, that "fluid" is air). The speed of sound in air is about 1100 feet per second, which is tough to demonstrate in a class since it's so fast. But any time you have waves moving in a medium, they move at a certain rate. If you take a big pan of water and touch the surface, the water waves move away forming a set of circular waves, and they move at some fixed speed that depends on the depth of the water, among other things. Next, drag your finger slowly across the surface of the water in a straight line and look at the shape of the rings. They are no longer uniformly spaced - those in front of your finger are more closely packed and those behind are spread out. If you move your finger a little faster, the waves in front are packed more and more closely, and when you move your finger at exactly the rate that the wave moves, the front edge of the waves is no longer curved - it becomes a cone with straight edges. If you move even faster, the cone just gets narrower. The edge of the cone is called a "shock wave" and since it's effectively made of a whole bunch of circular wave edges added together, it has a relatively large amount of energy, and when it hits things, they are more strongly affected than they would be by the ripples from just touching the water surface or from dragging your finger slowly. Sound is a 3D wave in air, and for a fixed noise, it forms a set of spherical waves going in all directions. For a slowly moving noise, the sphere is distorted, just as in the water, and when the noise is going as fast or faster than sound, it turns to a conical, high-energy shock-wave that can jolt your ear-drums, or even occasionally break windows. It's been a while since I was in third grade, so you'll have to use your judgement about how much math to put in. I'm pretty sure the kids can at least understand the explanation above. High-speed power boats make shock-waves all the time, and if you've ever gotten hit by the wake (shock-wave) of a big boat when you're in a little boat, it's obvious that it's different from just having some ripples pass you by. It's not hard (given the speed of the waves and the speed of your finger) to figure out the shape of the v-shaped shock-wave before you do it. The same thing can happen with light, but it's a little weird. Of course nothing can travel faster than the speed of light in a vacuum, but when light is travelling through certain substances, it does go significantly slower. Certain particle accelerators can get them going almost the speed of light in a vacuum, and if you then slam these particles into glass or something where light goes slower, you can actually make light shock-waves. Of course you need a few million dollars worth of accelerator to do this. -Doctor Tom, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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