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Q.

A closed organ pipe and an open organ pipe of same length produce $2 beats / s$ when they are set into vibrations together in fundamental mode. The length of open pipe is now halved and that of closed pipe is doubled. The number of beats produced will be

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a

$2$

b

$8$

c

$4$

d

$7$

answer is A.

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Detailed Solution

$\frac{v}{2 L} - \frac{v}{4 L} = 2 \Rightarrow \frac{v}{L} = 8$

$\frac{v}{2 (\frac{L}{2})} - \frac{v}{4 (2L)} = \frac{v}{L} (\frac{7}{8}) = 8 \times (\frac{7}{8}) = 7$

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