Question

The fundamental frequency of a closed pipe is $220 \,Hz$. If $\frac{1}{4}$ of the pipe is filled with water, the frequency of the first overtone of the pipe now is

• A. 220 Hz
• B. 440 Hz
• C. 880 Hz
• D. 1760 Hz

Answer 1

Answer: (C)

Fundamental frequency of closed pipe
$n=\frac{v}{4 l}=220 Hz $
$\Rightarrow v=220 \times 4 l$
If $\frac{1}{4}$ of the pipe is filled with water then remaining length of air column is $\frac{3 l}{4}$.
Now, fundamental frequency
$=\frac{v}{4\left(\frac{3 l}{4}\right)}=\frac{v}{3 l}$ and
First overtone $=3 \times$ fundamental frequency.
$=3 \times \frac{v}{3 L}=\frac{3 \times 220 \times 4 l}{3 l} $
$=880\, Hz$