Question

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

• A. 14
• B. 13
• C. 6
• D. 9

Answer 1

The correct option is C 6

Critical hearing frequency for a person is $20,000Hz$.
If a closed pipe is vibrating in $N^{th}$ mode, then frequency of vibration is going to be

$n=\frac{(2N-1)v}{4l}=(2N-1)n_1$, where $n_1$ is the fundamental frequency of vibration.

$⟹N=7.165\approx 7$

For a closed pipe,
number of overtones = (number of mode of vibration) - 1
$⟹$ number of overtones $=6$