A clsoed organ pipe and an open organ pipe of same length produce 2 beats /second while vibrating in their fundamental modes. The length of the open organ pipe is halved and that of closed pipe is doubled . Then the number of beats produced per second while vibrating in the fundamental mode is :

Options

A. 8
B. 7
C. 2
D. 6

Answer

B

Explanation

In first case `f_(0) - f_(c) = 2`.
`(v)/(2l) - (v)/(4l) = 2 `
`(v)/(4l) = 2 rArr (v)/(l) = 8 ` .
When length of open organ pipe is havlved and that of closed organ pipe is doubled then beat frequency will
`be f._(0) - f._(c) = (v)/(2. (i)/(2)) = (v)/(4.2) = (v)/(l) - (v)/(8l)`
= `(7)/(8) (v)/(l)`
= `(7)/(8) xx 8 = 7 ` Hz.
so correct choice is b.