Question

Use the formula v = (√ργ/ρ) to explain why the speed of sound in air increases with temperature.

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, $v=\sqrt{\frac{\gamma RT}{M}}$

here it is clear that speed of sound is directly proportional to square root temperature.
e.g., $v\propto\sqrt{T}$
therefore, speed of sound in air increases with temperature.