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The speed of sound in a gas may be given by the following formula,

$$c = (kRT)^{1/2},$$

where $k$ is specific heat ratio, $R$ is the gas constant and $T$ is the temperature.

  1. What are the limits of this formula? At very cold and very hot temperatures for instance?

  2. Would this formula be modified for near absolute zero temperatures?

  3. Likewise, What is the effect of very high pressure and very low pressure?

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  • $\begingroup$ Please consider writing descriptive question titles with appropriate punctuation, grammar, and formatting. See this meta post: How do we write good question titles?. I've edited it here. $\endgroup$
    – user191954
    Commented Oct 26, 2018 at 16:34

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The expression for the speed of sound is really:

$$ c = \sqrt{\left(\frac{\partial P}{\partial \rho}\right)_T} $$

Which is always true. The simplification you have listed is assuming an ideal gas. So the limits of that expression are the same as that for an ideal gas -- molecules interact only through collisions (no long-range forces) and the molecules have no volume.

If you are violating those assumptions at, say, high pressure or temperature, or in materials where there are long-range forces, then your expression won't work. And neither will the equation of state. But once you pick the appropriate equation of state, then the expression I gave will always be true.

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