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If second overtone of closed pipe and th...

If second overtone of closed pipe and third overtone of open pipe are equal, then find ratio of lengths of both the pipes.

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(i) For a closed pipe of length `L _(1),` second overtone = third harmonic `= (2n -1) f _(1)`
`= 5 xx ( v )/( 4 L _(1))`
`(because ` Here `n = 3 and f _(1) = (v)/( 4 L _(1)))…(1)`
(ii) For an open pipe of length `L _(2),`
third overtone = fourth harmonic `= nf._(1)`
`= 4 xx (v)/(2 L _(2))`
`(because ` Here ` n =4 and f ._(1) = (v)/(2 L _(2)))`
Now , as per the statement, `(5v)/( 4 L _(1)) = (4v )/( 2 L _(2))`
`therefore (L _(1))/( L _(2)) = (10)/( 16) = 5/8`
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