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 2nd overtone, `3/2f_0=(3V_0)/(2l)`
Let `f = (V_0)/(4l)` be the fundamental frequency of closed organ pipe. Third overtone of closed organ pipe at one end is
`f_3=7/(4)V_0/l`
As given, `(7V_0)/(4l)-(3V_0)/(2l)=150`
Rightarrow (7/4-6/4)V_0/l=150`
`Rightarrow `V_0/(4l)=150 Rightarrow V_0/(2l)=300Hz`