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Q.
An organ pipe 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 closed pipe produces only odd harmonics.
The frequency of note emitted from the pipe for $v$ being velocity of sound
in air, is
$ f'=n\left(\frac{v}{4 l}\right)$
and $l$ is length of pipe.
$f'=n \times$ fundamental frequency
$\therefore $ We know that human ear can hear
frequencies upto $20,000\, Hz$, hence
$20,000=n \times 1500$
$\Rightarrow n=\frac{20,000}{1500} \approx 13$
Maximum possible harmonics obtained are
$1,3,5,7,9,11,13$
Hence, man can hear upto $13^{th}$ harmonic
$=7-1=6$
So, number of overtones heard $ = 6$
