In the fundamental mode , time taken by the wave to reach the closed end of the air filled pipe is 0.01 s . The fundamental frequency is

Options

A. `(2t)^(-1)`
B. `4(t)^(-1)`
C. `2(t)^(-1)`
D. `(4t)^(-1)`

Answer

D

Explanation

As we know, the fundamental frequency for a closed organ pipe is given as,
`f_(0)=v/(4l)` ….(i)
where, v = velocity of sound wave inside the pipe and I= length of the pipe.
It is given that the time to reach the other end is t sec,
As, `t=l/v` ....(ii)
Hence, from Eqs. (i) and (ii), we get
`f_(0)=1/4dot1/t=(4t)^(-1)`
So, frequency of vibration of air coloumn is `4(t)^(-1)`.