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)

880 Hz

Answer 2

FundamentaI frequency of closed pipe \hspace25mm n =\frac{v}{4l}=220\, Hz \Rightarrow \hspace20mm v =220 \times 4l If $\frac{1}{4}$ of the pipe is filled with water then remaining length of air column is $\frac{3l}{4}.$ Now, fundamental frequency $=\frac{v}{4\big(\frac{3l}{4}\big)}=\frac{v}{3l}$ and First overtone= 3 $\times$ fundamental frequency. \hspace35mm = 3 \times \frac{v}{3L} =\frac{3 \times 220 \times 4l}{3l}= 880\, Hz