Question

The two nearest harmonics of a tube closed at one end and open at other end are $220Hz$ and $260Hz$. What is the fundamental frequency of the system?

• A. $20Hz$
• B. $30Hz$
• C. $40Hz$
• D. $10Hz$

Answer 1

The correct option is A $20Hz$

Frequency of $n$th harmonic vibration in closed pipe,
$V_n=\frac{2n-1}{4l}v=220Hz$
Frequency of $(n+1)$th harmonic vibration,
$V_{n+1}=\frac{\left[2\right(n+1)-1]}{4l}=\frac{(2n+1)v}{4l}$$=260Hz$

But $V_{n+1}-V_n=260-220=40$
$\frac{\left[\right(2n+1)-(2n-1\left)\right]v}{4l}=40$
$\frac{2v}{4l}=40$
$\Rightarrow \frac{v}{4l}=20Hz$
So the fundamental frequency of the system is $20Hz$.