A pipe of length `l_(1)`, closed at one end is kept in a chamber of gas of density `rho_(1)`. A second pipe open at both ends is placed in a second chamber of gas of density `rho_(2)`. The compressibility of both the gases is equal. Calculate the length of the second pipe if frquency of first overtone in both the cases is equal.

Options

A. `(4)/(3) l_1 sqrt((rho_2)/(rho_(1))`
B. `(4)/(3) l_1 sqrt(rho_1)/(rho_(2))`
C. `l_1 sqrt((rho_2)/(rho_(1))`
D. `l_1 sqrt(rho_1)/(rho_(2))`

Answer

B

Explanation

Frequency of first overtone in closed pipe,
`v = (3)/(4l_(1)) sqrt((B)/(rho_(1)))`…(i)
Frequency of the first overtone in open pipe,
`v = (1)/(l_(2)) sqrt((B)/(rho_(2))) rArr l_(2) =(4)/(3) l_(1) sqrt((rho_(1))/(rho_(2)))`….(ii).