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Q.

A closed organ pipe and an open organ pipe have their first overtone identical in frequency. Their lengths are in the ratio

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a

4:5

b

1:2

c

2:3

d

3:4

answer is C.

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Detailed Solution

detailed_solution_thumbnail

For first overtone of closed pipe
$n_{2} = \frac{3 V}{4 l_{1}}$
For first overtone of open pipe

$n_{2} = \frac{2 v}{2 l_{2}}$

$\frac{3 V}{4 l_{1}} = \frac{2 v}{2 l_{2}} or \frac{l_{1}}{l_{2}} = \frac{3}{4}$

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