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Question

An organ pipe closed at one end has a fundamental frequency of 1500 Hz. The maximum number of overtones generated by this pipe which a normal person can hear is

A
14
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B
13
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C
6
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D
7
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Solution

The correct option is C 6
Modes of vibration of air column in a closed organ pipe is given by

fn=(2n1)v4L where n=1,2,3,4.....

Fundamental frequency f0=v4L=1500 Hz

Normal person can hear sound of frequency upto 20,000 Hz.

Therefore, fn=(2n1)f0=20,000
1500×(2n1)=20,000
(2n1)=13.33
i.e (2n1)=13 [odd harmonics]
n=7

Total no. of modes of vibration that can be heard by the person is 7.
(6 overtones+1 Fundamental frequency

Thus, option (c) is the correct answer.

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