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)))`

Options

A. `(L)/(3)`
B. `(4L)/(3)`
C. `(4L)/(3) sqrt((rho_(1))/(rho_(2)))`
D. `(4L)/(3) sqrt((rho_(2))/(rho_(1)))`

Answer

C

Explanation

`f_(c) f_(0)` (both first overtone)
`rArr3((V_(c))/(4L))=2((V_(0))/(2l_(0)))`
`:. l_(0) =(4)/(3)((V_(0))/(V_(v)))L=(4)/(3)sqrt((rho_(1))/(rho_(2)))L` as `v prop (1)/(sqrt(rho))`