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

Options

A. ` 8`
B. `7`
C. `4`
D. `2`

Answer

B

Explanation

`f_(0) - f_( c) = 2`
or `(v)/( 2 l) - (v)/( 4 l) = 2 or (v)/( 4l) = 2`
or `(v)/( l) = 8`
When length of `OOP` is halved and that of `COP` is doubled , the beat frequency will be
`f'_(o) - f'_( c) = (v)/(l) - (v)/( 8 l) = ( 7)/(8) (v)/(l) = (7)/(8) xx 8 = 7`