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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 gass of densities `rho_(1)` and `rho_(2)`, respectively. The compressibility of gass are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency . The length of the open orange 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

`f _(C) = (nu)/(4((l_(0))/(2))) = (nu)/(2l_(0)) = f_(0) =f` (both first overtone)
or `3((nu_(C))/(4L)) = 2((nu_(0))/(2l_(0)))`
`:. l_(0) = (4)/(3) (nu_(0)/(nu_(C)))L = (4)/(3) (sqrtB//rho_(2))/(sqrtB//rho_(1)) L`
= `(4)/(3) sqrt((rho_(1))/(rho_(2))) L`
Hence, the correct option is (C).
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