Question

An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is found to be higher by `100 Hz` then the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is
A. (a) `200 Hz`
B. (b) `300 Hz`
C. ( c ) `240 Hz`
D. (d) `480 Hz`

Answer 1

Correct Answer - A
(a) For both end open
`(2lambda_(1))/(4) = l rArr lambda_(1) = 2l`
`v_(1) = ( c )/(lambda_(1)) = (c )/(2l)` …(i)
For one end closed
For third harmonic `(3lambda_(2))/(4) = l rArr lambda_(2) = (4l)/(3)`
`v_(2) = ( c )/(lambda_(2)) = (3c )/(4l)` …(ii)
Given `v_(2) - v_(1) = 100`
From (i) and(ii)
`(v_(2)/(v_(1) = (3//4)/(1//2) = (3)/(2)` ltbr. On solving, we get `v_(1) = 200 Hz`.