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 s^(-1)`
B. `100 s^(-1)`
C. `300 s^(-1)`
D. `250 s^(-1)`

Answer

a

Explanation

Frequency of second overtone (fifth harmonic) of
closed pipe `=(5v)/(2l)`
Accordingly, `(5v)/(4l)-(2v)/(2l)=100`
`rArr v/(4l)=100 or v = 400l`
Fundamental frequency of open pipe `=v/(2l)=(400l)/(2l)`
`=200 s^(-1)`