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`.

Explanation

Suppose the speed of sound in hydrogen is `v_(h)` and that in air is `v_(a)` The ftindamental frequency ofanorganpipe 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
`(v)/(500) = (v_(h))/(v_(a)) = sqrt((p_(a))/(p_(h))) = sqrt((1.2)/(0.089))` = 3.67
`v = 3.67 xx 500 approx 1840 Hz.`