Question

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

• A. $10\text{Hz}$
• B. $20\text{Hz}$
• C. $30\text{Hz}$
• D. $40\text{Hz}$

Answer 1

The correct option is B $20\text{Hz}$

We know that for a closed organ pipe, the resonate frequency is given by,
$f=\frac{nv}{4l}$
Fundamental frequency,
$f_o=\frac{v}{4l}$
Now, $f_n=\frac{nv}{4l}=220\text{Hz}$ ...........(1)
And successive frequency,
$f_{n+2}=\frac{(n+2)v}{4l}=260\text{Hz}$
$\Rightarrow \frac{nv}{4l}+\frac{2v}{4l}=260\text{Hz}$
$\Rightarrow 220+\frac{2v}{4l}=260\text{Hz}$
[from (1)]
$\Rightarrow \frac{2v}{4l}=40\text{Hz}$
$\Rightarrow f_o=\frac{v}{4l}=20\text{Hz}$