An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is found to be higher by `100 Hz` then the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is

Options

A. 100 Hz
B. 150 Hz
C. 200 Hz
D. 250 Hz

Answer

c

Explanation

For fundamental mode in open pipe,
and `v_(0)=v/21...(i)`
For third harmonic in closed pipe
`v=(2n+1)v/(4l)`
`n=1=(3v)/(4l)`
From Eqs. (i) and (ii), we have
`v-v_(0)=100` (given)
`rArr 3/2. v-v_(0)=100 ...(iii)`
`therefore v/2=100`
` rArr v_(0)=200 ` hz