# Why does a “speed of sound” exist?

I've recently read that wind cannot be faster than the speed of sound (german source).

But why is there a speed of sound? I understand (well, mostly accept to be honest) that the speed of light in vacuum is a maximal speed for all matter. And I understand that you need more energy the more you accelerate particles. But why can't you make wind faster?

There's a few things going on here. First of all, wind can move faster than the speed of sound.

As to your second question "Why is there a speed of sound"? Sound is caused by a change in position of molecules relative to a collection of other molecules. Since molecules have electrons on the outside, they are repulsed from one other (like charges repulse). Thus if you change the position of certain molecules, they will repulse the neighboring molecules. These neighboring molecules will then repulse their neighboring molecules, and thus you have this "shift in position" (usually measured as a shift in pressure) that propagates through space. This is what we hear as sound. The speed of propagation depends on how close the molecules are together when they are in equilibrium, the bonds the molecules have, etc.

For a simple understanding of sound, think of a bunch of train cars attached to one another through springs. Now push one end of the train a small amount. This push will compress the spring between train cars 1 and 2. The spring will then uncompress and push train 2 forward. This compresses the spring between trains 2 and 3. And so on... Until the last train car is moved forward. The total length of the train divided by the time it takes from the moment you push train car 1 till the last train car moves is the speed of sound (for train cars, note that the speed of sound is different depending on the material through which it moves - most often we refer to speed of sound as the speed of sound of air).

• I think he was asking why there is constant speed of sound, independent of the frequency/amplitude of the waves. – Anixx Dec 29 '13 at 23:03
• Wind is the flow of gases on a large scale. On the surface of the Earth, wind consists of the bulk movement of air through a larger mass of air at rest - the atmosphere which means that a wind tunnel is not wind . Also the Neptune winds are near supersonic speed. A supersonic airplane can comunicate with sound signals? NO. – Helder Velez Dec 30 '13 at 23:15

I've recently read that wind cannot be faster than the speed of sound

This is false. Wind can go faster than Mach 1. However, the wind present in nature usually doesn't, so the Fujita scale doesn't cross Mach 1.

But why is there a speed of sound?

Sound is, after all, a propagating vibration of air molecules. Molecules do not move around instantaneously; their speed is affected by the density and elasticity of the material — which in turn affect the speed of vibrations and thus sound.

I had a quick browse of the article and it doesn't seem to say that wind can't blow at greater than the speed of sound: it seems that the Fujita skale simply takes Mach 1 as its upper limit, most likely somewhat arbitrarily.

To get living examples of faster-than-sound winds, you only have to look at the gas giant planets. If you google something like "supersonic winds Saturn/Uranus/Neptune" you'll see a great deal of documented evidence for such winds. Some high end wind tunnels are also built to blow at greater than sound speed as the design of aircraft still depends heavily on experimental modelling - there's still a $US1M prize up for grabs from the Clay Mathematics Institute for a proof of (or counterexample against) the existence of globally smooth solutions to the Navier-Stokes equation, so it's not surprising that even now numerical simulation of aircraft flight is still very limited. There are no relativistic-type limits to particle velocities arising from the speed of sound. Sound has a medium, therefore the fundamental symmetry arguments that beget special realtivity (see the "From Group Postulates" section in the Wikipedia page for Lorentz Transformation do not hold. There is a privileged reference frame in sound wave analysis: that frame that is still with respect to the medium and the sound wave equation does not keep its basic D'Alembert form$(c_s^2 \nabla^2 - \partial_t^2)\psi=0$when you write it down in a frame of reference that is moving relative to the medium. Try it: if you substitute$x\to x+v\,t$you'll get a different equation. The Galilean relativity is adequate here: but if you go the "whole hog" and do a Lorentz transformation on it, you find the equation changes form unless$c_s = c$. I don't believe the Fujita scale is primarily meant to measure speed, but rather to get across an intuitive feel for a wind's destructiveness and even here it seems that building methods vary widely with different cultures so it makes the scale's application a bit moot. Fujita thought it up because the much older, and extremely useful, Beaufort scale gives out at about$100{\rm km h^{-1}}$winds, so cannot cope with tornados and cyclones. Since very few human built structures withstand even$300{\rm km h^{-1}}\$ winds, it would seem that Mach 1 is a very reasonable upper bound. One of the Fujita scale's uses is for planning and managing emergency responses: to give authorities an idea of what kind of an onslaught the hospitals are going to bear, how many people and other resources are going to be needed for a rescue and how many coffins to buy.