The fundamental of a closed pipe is 220 Hz. If `(1)/(4)` of the pipe is filled with water, the frequency of the first overtone of the pipe now is

Options

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

Answer

C

Explanation

Fundamental frequency of closed pipe
`n=(v)/(4l)=220Hzimpliesv=220xx4l`
if `(1)/(4)` of the pipe is filled with water then remaining length of air column is `(3l)/(4)`
now fundamental frequency `=(v)/(4((3l)/(4)))=(v)/(3l)` and First overtone`=3xx` fundamental frequency
`=(3v)/(3l)=(v)/(l)=(220xx4l)/(l)=880Hz`