Question

In a fundamental mode, the time required for the sound wave to reach upto the closed end of a pipe filled with air is $'t'$ second. The frequency of vibration of air column is

• A. $(2t)^{-1}$
• B. $4\,(t)^{-1}$
• C. $2(t)^{-1}$
• D. $(4\,t)^{-1}$

Answer 1

Answer: (D)

$(4\,t)^{-1}$

Answer 2

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