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In winter, the frequency of a tone emitt...

In winter, the frequency of a tone emitted at `10^(@)` C by an open organ tube is 400 Hz . What will be the frequency of this tone at `40^(@)` C in summer ?

Text Solution

Verified by Experts

Let ` V_(0)` be the velocity of sound in air at `0^(@)` C .
So , the velocity at `10^(@)` C ,
`V_(1) = V_(0) (1 + 0 . 00183 xx 10) = 1 . 0 183 V_(0)` ,
the velocity at ` 40^(@)` C ,
`V_(2) = V_(0) ( 1 + 0 . 00 183 xx 40) = 1 . 0 732 V_(0)`
The frequency of a tone is proportional to the velocity of sound .
` :. (n_(1))/(n_(2)) = (V_(1))/(V_(2))`
or , ` n_(2) = n_(1) * (V_(2))/(V_(1)) = 400 xx (1 . 0 73 2 V_(0))/(1 . 0 1 8 3 V_(0)) = 421 . 57 ` Hz .
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