Physics - Sound Wave Question with Solution | TestHub

The velocity of sound ($v$) and the root mean square velocity ($c$) in an ideal gas are both proportional to the square root of the absolute temperature ($T$).

$v\propto \sqrt{T}$ and $c\propto \sqrt{T}$

Therefore, $v_1/v_2=\sqrt{T_1/T_2}$ and $c_1/c_2=\sqrt{T_1/T_2}$.

This implies $v_1/v_2=c_1/c_2$, which rearranges to $c_2=c_1(v_2/v_1)$.