question_answer

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

Correct Answer: C

Solution :

Key Idea: A closed pipe produces only odd harmonics. The frequency of note emitted from the pipe for v being velocity of sound in air, is \[f=n\left( \frac{v}{4l} \right)\] and I is length of pipe.          \[f=n\times \] fundamental frequency \[\therefore \] We know that human ear can hear frequencies up to 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 up to 13th harmonic \[=7-1=6\] So, number of overtones heard = 6 Note: First overtone of the closed pipe is called the third harmonic.