Question

The third overtone of a closed pipe differs by $200H_Z$ from the first overtone of an open pipe what is the fundamental frequency of the closed pipe? Given length of the two pipes are l

• A. 40 Hz
• B. 50 Hz
• C. 60 Hz
• D. 70 Hz

Answer 1

The correct option is A 40 Hz

$3^{rd}$ overtone of closed pipe $=\frac{7v}{4l}$
$1^{st}$ overtone of open pipe $=\frac{v}{2l}$
$\frac{7v}{4l}-\frac{v}{2l}=\frac{5v}{4l}$

Now $\frac{5v}{4l}=200$
$\therefore \left(\frac{v}{4l}\right)=40Hz$ This is the fundamental frequency of the closed pipe.

Ans: 40Hz.