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Question

An open pipe is suddenly closed at one end as a result of which the frequency of the third harmonic of the closed pipe is found to be higher by 100Hz than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is

A
200Hz
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B
300Hz
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C
240Hz
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D
480Hz
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Solution

The correct option is A 200Hz
For an organ pipe open at both ends

fn=nv2L .....(1) where f stands for for pipe open at both ends

For an organ pipe closed at one end

fn=(2n1)v4L .....(2) where f' stands for for pipe closed at one end

From eqn(1)

f3=2v2L

From (2)

f3=5v4L

Given, f3f3=100

v4L=100

f1=v2L=2×v4L=2×100=200Hz

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