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

`v_(a)=500Hz, v_(H)=?, rho_(a)=1.20kg//m^(3)`
`rho_(H)=0.089kg//m^(3)`
Now, `(v_(H))/(v_(a))=(upsilon_(H))/(upsilon_(a))=sqrt((rho_(a))/(rho_(H)))=sqrt((1.20)/(0.089))=3.67`
`:.v_(H)=3.67v_(a)=3.67xx500=1835Hz`