An organ pipe is 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

Options

A. `14`
B. `13`
C. `6`
D. `9`

Answer

C

Explanation

Critical hearing frequency for a person is `20,000Hz`
If a closed pipe vibration in `N^(th)` mode then frequency of vibration
`n=((2N-1)v)/(4l)=(2N-1)n_1`
(where `n_1=` fundamental frequency of vibration)
Hence `20,000=(2N-1)xx1500impliesN=7.1approx7`
Maximum possible harmonics obtained are
`1,3,5,7,9,11,13`
Hence, man can hear up to `13^(th)` harmonic
`=7-1=6`
So, number of overtones heard `=6`