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Q.

The first overtone of an open organ pipe and the fundamental tone of a closed organ pipe give 5 beats per second when sounded together. If the length of the closed pipe is 25 cm, what are the possible lengths of the open organ pipe (Speed of sound in air = 340 m/sec) -

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a

98.5 cm and 101.5 cm

b

100 cm and 103 cm

c

90 cm and 100 cm

d

102 cm and 105 cm

answer is B.

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Detailed Solution

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For open organ pipe
$v_{1}$ = $\frac{2 v}{2 l_{1}} = \frac{v}{l_{1}}$
for closed organ pipe
$v_{0} = \frac{v}{4 l_{2}}$
$v_{1} - v_{0} = 5 H z \Rightarrow \frac{v}{l_{1}} - \frac{v}{4 l_{2}} = 5 H z$
$\Rightarrow l_{1}$ = 98.5 cm
Or $v_{0} - v_{1} = 5 H z \Rightarrow \frac{v}{4 l_{2}} - \frac{v}{l_{1}} = 5 H z$
$\Rightarrow l_{1}$ = 101.5 cm

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