At normal temperature and pressure, the speed of sound in air is 332 m/s. What will be the speed of sound in…
At normal temperature and pressure, the speed of sound in air is 332 m/s. What will be the speed of sound in hydrogen at normal temperature and pressure? (Air is 16 times heavier than hydrogen)
Solution
Sol. The speed sound in a gas is given by
$v=\sqrt{\gamma p/\rho}\ \Rightarrow\ \dfrac{v_a}{v_H}=\sqrt{\dfrac{\rho_H}{\rho_a}}$
$\Rightarrow\ \dfrac{\rho_H}{\rho_a}=1/16\ \Rightarrow\ \dfrac{v_a}{v_H}=\sqrt{1/16}=1/4$
$\Rightarrow\ v_H=4v_a=4\times332=1328\ \mathrm{m/s}$
Answer: $1328$ ms$^{-1}$