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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 gases of densities `rho_1` and `rho_2` resp. The compressiblity of gases are equal in both pipes. Both pipes are vibrating in first overtones with same frequency. The length of open organ pipe is

A

`L/3`

B

`(4L)/3`

C

`(4L)/3sqrt(rho_1/rho_2)`

D

`(4L)/3sqrt(rho_2/rho_1)`

Text Solution

Verified by Experts

The correct Answer is:
C
`1^(st)` overtone in closed pipe `f=3/(4l_1)sqrt((gammaP)/(rho_1))`
`1^(st)` Overtone is open pipe : `f.=(1)/(l_2)sqrt((gammaP)/(rho_2))`
Now, f = f.
`implies 3/(4l_1) = sqrt((gammaP)/(rho_1))=1/(l_2)sqrt((gammaP)/(rho_2))`
`implies l_2=(4l_1)/3sqrt((rho_1)/(rho_2))impliesl_2=(4L)/3sqrt((rho_1)/(rho_2))`
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