First slide

Stationary waves

Question

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

Difficult

A

14
B

13
C

6
D

9

Solution

Critical hearing frequency for a person is 20,000Hz.
If a closed pipe vibration in N^th mode then frequency of vibration $n = \frac{(2 N - 1) v}{4 l} = (2 N - 1) n_{1}$
(where n₁ = fundamental frequency of vibration)
Hence 20,000 $= (2 N - 1) \times 1500 \Rightarrow N = 7 .1 \approx 7$
Also, in closed pipe
Number of over tones = (No. of mode of vibration) –1
= 7 – 1 = 6.

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