An open pie is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is found to be heigth by `100 H_(Z)` than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is
(a) `200 H_(Z)` (b) `300 H_(Z)` (c ) `240 H_(Z)` (d) `480 H_(Z)`

Options

A. 200Hz
B. 300Hz
C. 240Hz
D. 480 Hz

Answer

A

Explanation

Length of the organ pipe is same in both the cases. Fundamental frequency of open pipe is `f_(1)=(v)/(21)` and frequency of third harmonic of closed pipe will be `f_(2)=3((V)/(41))`
Given that, `f_(2)=f_(1)+100`
`f_(2)-f_(1)=100,(3)/(4)((v)/(1))-((1)/(2))((v)/(1))=100`
`(v)/(41)=100Hz, (v)/(21) or f_(1)=200Hz`
Therefore, fundamental frequency of the open pipe is 200 Hz.