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» <html><body><p></p><a href="https://interviewquestions.tuteehub.com/tag/solution-25781" style="font-weight:bold;" target="_blank" title="Click to know more about SOLUTION">SOLUTION</a> :(i) For a closed pipe of length `L _(1),` second <a href="https://interviewquestions.tuteehub.com/tag/overtone-1144273" style="font-weight:bold;" target="_blank" title="Click to know more about OVERTONE">OVERTONE</a> = third harmonic `= (2n -1) f _(1)` <br/> `= 5 <a href="https://interviewquestions.tuteehub.com/tag/xx-747671" style="font-weight:bold;" target="_blank" title="Click to know more about XX">XX</a> ( v )/( <a href="https://interviewquestions.tuteehub.com/tag/4-311707" style="font-weight:bold;" target="_blank" title="Click to know more about 4">4</a> L _(1))` <br/> `(because ` Here `n = 3 and f _(1) = (v)/( 4 L _(1)))…(1)` <br/> (ii) For an open pipe of length `L _(2),` <br/> third overtone = <a href="https://interviewquestions.tuteehub.com/tag/fourth-998521" style="font-weight:bold;" target="_blank" title="Click to know more about FOURTH">FOURTH</a> harmonic `= nf._(1)` <br/> `= 4 xx (v)/(2 L _(2))` <br/> `(because ` Here ` n =4 and f ._(1) = (v)/(2 L _(2)))` <br/> Now , as per the statement, `(5v)/( 4 L _(1)) = (4v )/( 2 L _(2))`<br/> `therefore (L _(1))/( L _(2)) = (10)/( 16) = 5/8`</body></html>