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

`1000sqrt(14) Hz`

Explanation

Suppose the speed of sound in hydrogen is `v_(H)` and that in nitrogen is `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
`(n)/(1000 Hz) = (v_(H))/(v_(N)) = sqrt((M_(N))/(M_(H)))` (Since both `N_(2)` and `H_(2)` are diatomic, `gamma` is same for both)
or, `(n)/(1kHz) = sqrt((28)/(2)) rArr n = 1000sqrt(14) Hz`.