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

A closed organ pipe and an open organ pipe of same length produce 2 beats when they are set into vibrations simultaneously in their fundamental mode. The length of open organ pipe is now halved and of closed organ pipe is doubled, the number of beats produced wil be
(A)8 (B)7 (C)4 (D)2

A

8

B

7

C

4

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
`f_(0)-f_(c)=2`
or `(v)/(2l)-(v)/(4l)=2 or (v)/(4l)=2 or (v)/(l)=8 ` . . . (i)
When length of open organ pipe is halved and that of closed organ pipe is doubled. The beat frequency will be
`f_(0)'-f_(c)'=(v)/(l)-(v)/(8l)=(7)/(8)(v)/(l)`
Substituting `(v)/(l)=8` from equation (i) beat frequency=7.
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