Question

A closed organ pipe and an open pipe of same length produce 4 beats when they are set into vibrations simultaneously. If the length of each of them were twice their initial lengths, the number of beats produced will be [Assume same mode of vibration in both cases]

• A. 2
• B. 4
• C. 1
• D. 8

Answer 1

The correct option is A 2

Given,

Beat frequency = 4

We have,

Beat frequency = difference between the two frequency

That is,

$4=f_{open}-f_{closed}$

$4=\frac{f}{2L}-\frac{f}{4L}=\frac{f}{2L}$

where $L$ is the length of the pipes.

When the length of the pipes becomes twice, the beat produced $B$

will be,

$B=\frac{f}{4L}-\frac{f}{8L}=\frac{f}{4L}$

$\frac{B}{4}=\frac{f}{4L}\times \frac{2L}{f}=\frac{1}{2}$

That is,

$B=\frac{4}{2}=2$

Hence t6he correct answer is $2$.