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A closed organ pipe of length L and an o...

A closed organ pipe of length `L` and an open organ pipe contain gasses of densities `rho_(1)` and `rho_(2)`, respectively. The compressibility of gasses are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency . The length of the open organ pipe is
(a) `(L)/(3)`
`(4l) / (3)`
(c ) `(4l)/(3)sqrt((rho_(1))/(rho_(2)))`
(d) `(4l)/(3)sqrt((rho_(2))/(rho_(1)))`

Text Solution

Verified by Experts

Frequency of first overtone is closed pipe `f=(3)/(4l_(1)) sqrt((P)/(rho_(1)))` Frequency of first overtone in open pipe
`f^(1)=(1)/(l_(2)) sqrt((p)/(rho_(2))) rArr l_(2)=(4)/(3)l_(1) sqrt((rho_(1))/(rho_(2)))`
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