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If speed of sound is 330 m/s. The lengths of closed pipe and open pipe are :

Answer»

0.4125 m, 1.65m
3.3m, 1.65m
0.825m, 0.825m
1.65m, 0.825m

Solution :For CLOSED pipe,
`3^(rd)` overtone = `7^(th)` harmonic = `n_(7) = (7v)/(4l_(c))`
`5^(th)` harmonic `n_(5) = (5v)/(4l_(c))`
`n_(7) - n_(5) = (2v)/(4l_(c))` = 400 Hz implies `n_(0) = (v)/(4l_(c)) = 200 Hz` (fundametal frequency of closed pipe) Now `3^(rd)` harmonicof closed pipe is equal to `6^(th)` harmonic of open pipe
`(v)/(4l_(c)) = (6v)/(2l_(0))`
implies`(v)/(l_(0)) = (v)/(4l_(c))` = 200 Hz
FUNDAMENTAL frequency of open pipe = `(v)/(2l_(0))` = 100 Hz
Further `l_(0) = (330)/(4 xx 200)` = 0.4125 m
`l_(0) = (330)/(2 xx 100)` = 1.65 m


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