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. 4
B. 13
C. 6
D. 9

Answer

C

Explanation

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((v)/(4 l))`
and `l` is length of pipe.
`f' = n xx` fundamental frequency
`:.` We know that human earcan hear frequencies upto `20,000 Hz`, hence
`20,000 = n xx 1500`
`rArr n = (20,000)/(1500) ~~ 13`
Maximum possible harmonics obtained are
`1,3,5,7,9,11,13`
Hence, man car hear upto `13th` harmonic
`= 7 - 1 = 6`
So, number of overtones heard `= 6`.