Question

A certain organ pipe resonates in its fundamental mode at a frequency of 500 Hz in air. What will be the fundamental frequency if the air is replaced by hydrogen at the same temperature? The density of air is `1.20kgm^-3` and that of hydrogen is `0.089 kgm^-3`.

Answer 1

Suppose the speed of sound in hydrogen in `v_h` and that in aire is v_a.` The fundamental frequency of an organ pipe is proportioN/Al to the speed of sound in the gas contained in it. If the fundamental frequency with hydrogen in the tube is v we have
`v/(500Hz)=v_h/v_a=sqrt(rho_a/rho_h)=sqrt(1.2/0.089)=3.67`
or `v=3.67xx500Hz~~1840Hz`.