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Show that if the room temperature change...

Show that if the room temperature changes by a small amount from `T to T +/_\T`, the fundamental frequency of an organ pipe changes from `v to v + /_\v, where
`(/_\v)/v=1/2(/_\T)/T`.

Text Solution

Verified by Experts

The correct Answer is:
A
We know that `fpropsqrtT`
According to the questioin
`f+/_\fprop sqrt(/_\T+T)`
`rarr (f+/_\f)/f=sqrt(/_\T+T)/T)`
`rarr 1+(/_\f)/f=(1+(/_\T)/T)^(1/2)`
`=1+1/2 (/_\T)/T`
`……. (neglecting other terms) `
`rarr (/_\f)/f=(1/2)(/_\T)/T`
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