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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 6Modes of vibration of air column in a closed organ pipe is given by fn=(2n−1)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=(2n−1)f0=20,000 ⇒1500×(2n−1)=20,000 ⇒(2n−1)=13.33 i.e (2n−1)=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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