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

Frequency of first over tone of closed pipe `=` frequency of first overtone of open pipe
`implies(3v)/(4L_1)=(v)/(L_2)implies(3)/(4L_1)sqrt((gammaP)/(rho_1))=(1)/(L_2)sqrt((gammaP)/(rho_2))`
`:. L_2=(4)/(3)Lsqrt((rho_1)/(rho_2)): "[:. V= sqrt((gammaP)/( p))]`.