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We know the speed depends on the kinetic energy. Imagine that we have 3 iron balls equally spaced and kept in space (zero gravity condition).

If i push the first ball slowly it would travel slowly and hit the middle ball and it would travel much more slower to hit the final ball. But if i had pushed the first ball with higher energy the collision would have been much faster.

But why isn't this happening with air? We know air molecules are spaced and if i push air with higher velocity, why wouldn't the speed of sound increase?

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The molecules in air are not sitting still waiting for your push. Because of thermal energy, they are moving quite rapidly (close to 1,000 miles per hour). Your push will not significantly increase the speed of sound unless you push hard enough to raise the gas temperature. Pushing that hard would be very unpleasant on your ear drums.

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  • $\begingroup$ At least why won't the speed slow down over distance? $\endgroup$
    – AlphAether
    Commented Jul 10, 2015 at 6:57
  • $\begingroup$ The sound speed would slow down over distance only if the gas was colder at that distance. Compared to the thermal energy of the gas, the energy supplied by your push is just too small to matter. $\endgroup$
    – John1024
    Commented Jul 10, 2015 at 7:00
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You can, in non-perfect gasses (which is basically all real-life gases). Your higher push, will result in different frequency sound and the speed will be different by a very small and negligible amount.

The example you provided, is an extreme case of a non-perfect gas, that is why you notice the change so much. The speed of iron balls is almost zero and your simulated sound is causing them to move much much faster.

In real-life gases, the change in the speed of the molecules is very little compared to their normal speed.

Remember sound is just a pressure wave. we know PV relates to v(speed) by the power of 2. It means changes in pressure causes very little change in speed

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