Physics - Sound Wave Question with Solution | TestHub

Let the length of the closed pipe be $L$.

The time taken by the sound wave to travel the length of the pipe is $t$.

The speed of the sound wave is $v=\frac{L}{t}$.

In the fundamental mode of a closed pipe, the length of the air column is related to the wavelength $\lambda$ by $L=\frac{\lambda }{4}$.

The frequency of vibration is given by $f=\frac{v}{\lambda }$.

Substituting $v=\frac{L}{t}$ and $\lambda =4L$, we get:

$f=\frac{L/t}{4L}=\frac{1}{4t}=\frac{0.25}{t}$

Answer: $\frac{0.25}{t}$