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A closed organ pipe and an open organ pi...

A closed organ pipe and an open organ pipe of some length produce ` 2 beats ` when they are set up into vibration simultaneously in their fundamental mode . The length of the open organ pipe is now halved and of the closed organ pipe is doubled , the number of beats produced will be a) 7 b) 4 c) 8 d) 2

Text Solution

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The correct Answer is:
`7`
`f_(0) - f_(c ) = 2`
`V[(1)/(2 L) - (1)/( 4 L)] = 2 or V//L = 8`
In the second case , `f'_(0) - f'_( c ) = (V)/(L) - (V)/( 8 L) = ( 7 V)/( 8 L) = (7)/(8) (8) = 7`
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