Question

Use the formula v = (√ργ/ρ) to explain why the speed of sound in air is independent of pressure.

Answer 1

speed of sound is given by $v=\sqrt{\frac{\gamma P}{\rho}}$
where v is the speed of sound in air,
$\gamma$ is adiabatic coefficient
P is pressure and $\rho$ is density
we know, for ideal gas equation,
$\rho=\frac{PM}{RT}$

so, speed of sound, $v=\sqrt{\frac{\gamma RT}{M}}$

Since, R is a constant, For constant Temperature, PV is constant.
we see that γ and M are also constant,
So it can be concluded that, velocity of sound is constant at constant temperature, it is not affected by change in pressure