1.

An organ pipeP_1 , closed at one end and containing a gass of densityP_1 is vibrating in the harmonic. Another organ pipe P_2 is vibrating in its third harmonic. Both the pipes are in resonance with a giventuning fork. If the compressbility of gases is equal in both pipes, the ratio of the lenghth ofP_1 and P_2 (assume the given gases to be monoatonic).

Answer»

`1/3`
3
`1/6sqrt(P_1)/(P_2)`
`1/6sqrt(P_2)/(P_1)`

SOLUTION :For an open ORGAN PIPE,
`n_1=(3V_2)/(2l_2)`
At RESONANCE ,`n_1=n_3`
`implies V_1/(4l_1)=(3V_2)/2L_2`
`implies l_2/l_1=6xxsqrt(B/P_2)SQRT(P_1)/B`
`implies l_1/l_2=1/6sqrt(P_2)/P_1`


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