A closed organ pipe and an open pipe of same length produce 2 beats $s^{- 1}$ 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

Question

Dr. Abubacker · Accepted Answer

(a) $n_{c} = \frac{v}{4l},\ n_{0} = \frac{v}{2l}$
As $n_{0} - n_{c} = 2$
$	herefore\frac{v}{2l} - \frac{v}{4l} = 2\ or\frac{v}{l} = 8$
Now $n_{0}^{'} = \frac{v}{2l/2} = \frac{v}{l}\ and\ n_{c}^{'} = \frac{v}{4(2l)} = \frac{v}{8l}$
Number of beats $s^{- 1} = n_{0}^{'} - n_{c}^{'}$
$= \frac{v}{l} - \frac{v}{8l} = \frac{7v}{8l} = \frac{7}{8} 	imes 8 = 7$

Q. A closed organ pipe and an open pipe of same length produce 2 beats $s^{- 1}$ 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

Explanation

Reviewed by Dr. Abubacker

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