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Q.

Third overtone of a closed organ pipe is in unison with fourth harmonic of an open organ pipe. Find the ratio of the lengths of the pipes.

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a

$\frac{l_{}}{l_{o}} = \frac{7}{8}$

b

$\frac{l_{c}}{l_{o}} = \frac{7}{8}$

c

$\frac{l_{c}}{l_{o}} = \frac{7}{5}$

d

$\frac{l_{c}}{l_{o}} = \frac{9}{8}$

answer is B.

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Detailed Solution

Third overtone of closed organ pipe means seventh harmonic. Given

${(f_{7})}_{closed} = {(f_{4})}_{open}$

$7 (\frac{v}{4 l_{c}}) = 4 (\frac{v}{2 l_{o}})$

$\frac{l_{c}}{l_{o}} = \frac{7}{8}$

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Third overtone of a closed organ pipe is in unison with fourth harmonic of an open organ pipe. Find the ratio of the lengths of the pipes.