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

Answer 1

The correct option is C $20Hz$

Frequency of nth harmonic vibration in closed pipe
$V_n=\frac{2n-1}{42}v=220$
Frequency of $n+1^{th}$ harmonic vibration
$V_{n+1}=\frac{\left[2\right(n+1)-1]}{42}=\frac{\left(\right(2n+1)v}{42}=260Hz$
But $V_{n+1}-V_n=260-220$
$\frac{\left[\right(2n+1)-(2n-1\left)\right]v}{42}=40$

$\frac{2v}{42}=40$

$\frac{v}{42}=20Hz$
So the fundamental frequency of the system is $20Hz$.

Hence C is the correct answer.