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 :

A closed pipe produces only odd harmonics. The frequency of note emitted from the pipe for v being velocity of sound in air is \[f'=n\left( \frac{\nu }{4l} \right)\] and l is length of pipe. \[\operatorname{f} \,=\,\,n\,\,\times \,\,fundamental frequency\] \[\therefore \] 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 \[=\text{ }6\]