Question

Fundamental frequency of a organ pipe filled with $N_2$ is 1000 Hz. Find the fundamental frequency if $N_2$ is replaced by $H_2$ :

Answer 1

Let the speed of sound in hydrozen be $v_h$ and in nitrogen be $v_n$

The fundamental frequency of an organ pipe is proportional to the speed of sound in the gas contained in it. If the fundamental frequency with hydrogen in the tube is v, we have

$\frac{n}{1000}=\frac{v_H}{v_N}=\sqrt{\frac{M_H}{M_N}}$

since nitrozen and hydrogen are diatomic both will have same $\gamma$

$\frac{n}{1000}=\sqrt{\frac{28}{2}}=\sqrt{14}$

$n=1000\sqrt{14}Hz$