Q: 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 than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is
(a) 200 Hz
(b) 300 Hz
(c) 240 Hz
(d) 480 Hz
Ans: (a)
Sol: Fundamental frequency of open pipe is
$\large f_1 = \frac{v}{2l}$
Third harmonic of closed pipe is
$\large f_2 = 3(\frac{v}{4l} ) $
According to question ;
$\large f_2 = f_1 + 100 $
$\large f_2 – f_1 = 100 $
$\large 3(\frac{v}{4l} ) – \frac{v}{2l} = 100 $
$\large \frac{v}{4 l} = 100 $
Hence ,$\large \frac{v}{2 l} = 200 $
The fundamental frequency of the open pipe is 200 Hz