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)/(4//) =220 Hz`
`rArr v = 220 xx 4//`
if `(1)/(4)`th of the pipe is filled with water then remaining length of air column is `(3//)/(4)`.
Now, overtone = `3xx` fundamental frequency
` 3 xx (v)/(3L) = (3xx 220 xx4//)/(3//)`
` = 880 Hz`