An open organ pipe is closed suddenly with the result
that the second overtone of the closed pipe is found
to be higher in frequency by 100 than the first
overtone of the original pipe. Then, the fundamental
frequency of the open pipe is

Options

A. 200 per sec
B. 100 per sec
C. 300 per sec
D. 250 per sec

Answer

A

Explanation

Frequency of second overtone (fifth hormonic) of closed pipe `=(5v)/(4l)`
Frequency of first overtone (second harmonic) of open pipe
`=(2v)/(2/)`
Accordingly, `(5v)/(4)-(2v)/(2.)=100`
or `(v)/(4)=100 or v=400/`
Fundamental frequency of open pipe
`=(v)/(2.)=(400.)/(2L)=200` per sec