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The length of an organ pipe open at two ...

The length of an organ pipe open at two ends is twice that of another organ pipe closed at one end . If the fundamental frequency of the open pipe is 100 Hz , find out the frequency of the 3rd harmonic emitted by the closed pipe .

Text Solution

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The fundamental frequency of the open pipe, `n_(0^(.)) = (V)/(2l),so V = 2ln_(0^(.))` [V = velocity of sound in air, l = length of the open pipe]
The length of the closed pipe is `(l)/(2)` . So the frequency of the 3rd harmonic is
` n = 3 xx ` fundamental frequency
`= 3n_(0) = 3* (V)/(4(1/2))=(3.2V)/(4)`
`=(3xx2xx2ln0^(.))/(4l)=3n_(0)^(.)`
` = 3 xx 100 = 300 ` Hz .
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