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37.An organ pipe P_{1} closed at one end vibrating in its first overtone and another pipe P_{2}open at both ends vibrating in third overtone are in resonance with a given tuning fork. The ratio of the length P_{1}to that of P_{2}is --------

**First overtone of Closed organ pipe P1:**

It is equal to 3rd harmonic.

${f}_{1}=\frac{3v}{4{L}_{1}}\phantom{\rule{0ex}{0ex}}Here,visspeedofsoundand{L}_{1}islengthofpipe{P}_{1}$

**Third overtone of open organ pipe P2:**

It is equal to 4th harmonic.

${f}_{2}=\frac{4v}{2{L}_{2}}\phantom{\rule{0ex}{0ex}}=\frac{2v}{{L}_{2}}\phantom{\rule{0ex}{0ex}}Here,visspeedofsoundand{L}_{2}islengthofpipe{P}_{2}$

**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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