Question

An open pipe is suddenly closed at one end and with the result frequency of third harmonic of the closed pipe is found to be higher by 100 Hz than the fundamental frequency of the open pipe. What is the fundamental frequency of the open pipe?

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

Answer 1

The correct option is A

200 Hz

For both ends open, fundamental frequency

$\frac{2{\lambda }_1}{4}=l\Rightarrow {\lambda }_1=2l$

$\therefore v_1=\frac{c}{{\lambda }_1}=\frac{c}{2l}\dots \left(i\right)$

For end closed the third harmonic

$\frac{3{\lambda }_2}{4}=l\Rightarrow {\lambda }_2=\frac{4l}{3}$

$v_2=\frac{c}{{\lambda }_2}=\frac{3c}{4l}\dots \left(ii\right)$

From question

$\frac{3c}{4}l=100+\frac{c}{2l}$

$\frac{c}{2l}=200Hz$.