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Question

Two narrow organ pipes, one open (length l1) and the other closed (length l2) are sounded in the respective fundamental modes. The beat frequency heard is 5 Hz. If now the pipes are sounded in the first overtones, then also the beat frequency heard 5 Hz. Then



A

l1l2=12

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B

l1l2=11

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C

l1l2=32

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D

l1l2=23

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Solution

The correct option is Bl1l2=11.

The harmonic frequencies in an open pipe are given by,

νn=nv2l1

and that for a closed pipe are given by

νn=(2n1)v4l2

For the beat frequency in fundamental mode:

v2l1v4l2=5............(1)

For the beat frequency in first overtone:

2(v2l1)3(v4l2)=5.......(2)
From Eqs. (1) and (2) we get,
l1l2=11=1:1.


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