37.An organ pipe P1 closed at one end vibrating in its first overtone and another pipe P2open at both ends vibrating in third overtone are in resonance with a given tuning fork. The ratio of the length P1to that of P2is --------

First overtone of Closed organ pipe P1:

It is equal to 3rd harmonic.

Third overtone of open organ pipe P2:

It is equal to 4th harmonic.

Equate f1 and f2 to find the ratio of lengths: (condition of resonance)

$\frac{3v}{4{L}_{1}}=\frac{2v}{{L}_{2}}\phantom{\rule{0ex}{0ex}}\frac{3}{4{L}_{1}}=\frac{2}{{L}_{2}}\phantom{\rule{0ex}{0ex}}8{L}_{1}=3{L}_{2}\phantom{\rule{0ex}{0ex}}\frac{{L}_{1}}{{L}_{2}}=\frac{3}{8}$

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