Question

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. 4
• B. 13
• C. 6
• D. 9

Answer 1

Answer: (C)

6

Answer 2

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 $= 6$