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

If second overtone of closed pipe and third overtone of open pipe are

1.	If second overtone of closed pipe and third overtone of open pipe are equal, then find ratio of lengths of both the pipes.
Answer» SOLUTION :(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`