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


For open pipe, in fundamental mode,
$l=\frac{{\lambda }_1}{2}$
$\therefore Frequency=\frac{v}{{\lambda }_1}=\frac{v}{21}\therefore v_1=\frac{v}{2I}......(i$

For closed pipe, vibrating in third harmonic,
$I=\frac{3{\lambda }_2}{4}$
$\therefore Frequency$
$=\frac{v}{{\lambda }_2}=\frac{3v}{4I}$
$or{v}_2=\frac{3v}{4I}$
$v_2-v_1=100\left(given\right)$
$\therefore \frac{3v}{4I}-\frac{v}{2I}=100or\frac{v}{4I}=100orv=400I$
$\therefore v_1=\frac{v}{2I}=\frac{400l}{2I}=200Hz$
$\therefore$ Fundamental frequency of open pipe = 200 Hz