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The length of an open orgen pipe is twi...

The length of an open orgen pipe is twice the length of a closed organ pipe. If the fundamental frequency of the open pipe is 100 Hz , what is the frequency of the third harmonic of the closed pipe ?

Text Solution

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Let the length of the closed organ pipe = l .
` :.` Length of the open organ pipe = 2 l .
Frequency of the fundamental of the open pipe, `n_(0) = (V)/ (2 . 2l) = (V)/(4l) ` [V = velocity of sound in air ]
or , ` l = (V)/(4n_(0)) = (V)/(4 xx 100) = (V)/(400)`
Frequency of the fundamental of the closed pipe,
` n_(c) = (V)/(4l) = (V)/(4)* (400)/(V) = 100 ` Hz
Only the odd harmonics are produced from a closed pipe , so the frequency of the third harmonic ` = 100 xx (3 xx 2 - 1) = ` 500 Hz .
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