Question

An organ pipe 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

• A. 4
• B. 13
• C. 6
• D. 9

Answer 1

Answer: (C)

A closed pipe produces only odd harmonics.
The frequency of note emitted from the pipe for $v$ being velocity of sound
in air, is
$f^{\prime }=n\left(\frac{v}{4l}\right)$
and $l$ is length of pipe.
$f^{\prime }=n\times$ fundamental frequency
$\therefore$ We know that human ear can hear
frequencies upto $20,000Hz$, 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 $=6$