Question

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

Answer 1

Given that fundamental frequency, $n_1=1500Hz$

Maximum hearing frequency for a person, $n=20000Hz$

For a closed pipe vibration in $N^{th}$ mode then frequency of vibration,

$\Rightarrow n=\frac{(2N-1)}{4l}$

$\Rightarrow n=(2N-1)n_1$

$\Rightarrow 20000=(2N-1)\times 1500$

$\Rightarrow (2N-1)=13.33$

$\Rightarrow 2N=14.33$

$\Rightarrow N=7.1\approx 7$

For closed pipe,

$\Rightarrow$ Number of overtones ~$=N-1$

$=7-1=6$

Final Answer: $6$