Question

The fundamental frequency of a closed pipe is 220 Hz. If $\frac{1}{4}$ th 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 for a closed organ pipe is $n=\frac{v}{4l}$ When one-fourth of the pipe is filled with water, then New length $l=l-\frac{l}{4}=\frac{3l}{4}$ $\therefore$ New frequency $n=\frac{v}{4l}$ $=\frac{v}{4\times \frac{3l}{4}}=\frac{v}{3l}$ $\frac{n}{n}=\frac{v/3l}{v/4l}$ $n=\frac{4}{3}n$ $=\frac{4}{3}\times 220=\frac{830}{3}Hz$ For closed organ pipe, first overtone $=3\times$ fundamental frequency = 3n $=3\times \frac{880}{3}=880Hz$