When open pipe is closed from one end, then third overtone of closed pipe is higher in frequency by 150 Hz than second overtone of open pipe. The fundamental frequency of open end pipe will be

Options

A. 75 Hz
B. 150 Hz
C. 225 Hz
D. 300 Hz

Answer

d

Explanation

According to question, fundamental frequency of
organ pipe is given by `f_(0)=v_(0)/(2l)`
[Symbols have their usual meanings]
In 2nnd overtone, `3/2f_(0)=(3v_(0))/(2l)`
Let `f=v_(0)/(4l)` be the fundamental frequency of closed organ
pipe. Third overtone of closed orosed organ pipe at one end is
`f_(3)=7/4 v_(0)/l`
As given, `(7v_(0))/(4l)-(3v_(0))/(2l) = 150`
`rArr (7/4-6/4)v_(0)/l=150`
`rArr v_(0)/(4l)=150`
`rArr v_(0)/(2l)=300` Hz