Q. 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
A) 14
B) 13
C) 6
D) 9
Explanation
(c) Critical hearing frequency for a person is $20,000Hz.$
If a closed pipe vibration in $N^{th}$ mode then frequency of vibration
$n = \frac{(2N - 1)v}{4l} = (2N - 1)n_{1}$
(where $n_{1} =$ fundamental frequency of vibration)
Hence $20,000 = (2N - 1) \times 1500$
$\Rightarrow N = 7.1 = 7$
Also, in closed pipe
Number of over tones $=$ (No. of mode of vibration)$\ - 1$
$= 7 - 1 = 6$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.