A closed organ pipe of length 'L' and an open organ pipe contain gases of densities `rho(1) and rho_(2)` respectively . The compressibility of gases are equal in both the pipes . If the frequencies of their first overtones are same then, the length of the open organ pipe is

Options

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

Answer

B

Explanation

For closed organ pipe
` f = f_(2) = 3f_(1)`
` = (3 xx v)/(4L) = (3)/(4L) xx sqrt((gammaP)/(rho_(1)))`
For open organ pipe,
`f = f_(2) = 2f_(1) = (2v)/(2L.)=(v)/(L.)`
`= (1)/(L.) xx sqrt((gammap)/(rho_(2)))`
for same sound frequency
`(3)/(4L) xx sqrt((gamma p)/(rho_(1)))=(1)/(L.)xx sqrt((gammap)/(rho_(2)))`
`:. L. = (4L)/(3) xx sqrt((rho_(1))/(rho_(2)))`