The two nearest harmonics of a tube closed at one end and open at other end are 220 Hz and 260 Hz. What is the fundamental frequency of the system?

Options

A. 10 Hz
B. 20 Hz
C. 30 Hz
D. 40 Hz

Answer

B

Explanation

Let fundamental frequency of the vibration is n

For a closed pipe,
`(lambda)/(4) = l " "rArr lambda = 4l`
`upsilon = v lambda`
`upsilon = v 4l rArr (n upsilon)/(4l) = 220` Hz
For a closed organ pipe, the frequencies of harmonics is in ratio of
`v_(1) : v_(2) : v_(3).... = 1 : 3 : 5....`
The successive frequency of closed pipe is
`((n + 2)upsilon)/(4l) = 260` Hz
`(n+2)/(n) = (260)/(220)`
22n + 44 = 26n
n = 11
As `(n upsilon)/(4l) = 220`
`therefore" "(upsilon)/(4l) = 20 or n = 20` Hz