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 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

Answer 1

The correct option is A

200 Hz

Length of the organ pipe is same in both the cases. Fundamental frequency of open pipe is $f_1=\frac{V}{2l}$ frequency of third harmonic of closed pipe will be

Given that $f_2=f_1+100$

or $f_2=f_1+100$

or $\frac{3}{4}(\frac{v}{l})-(\frac{1}{2})(\frac{v}{l})=100$

$\Rightarrow \frac{v}{4l}=100Hz$

$\therefore \frac{v}{2l}or{f}_1=200Hz$

Therefore, fundamental frequency of the open pipe is 200 Hz.