In fundamental mode, the time required for the sound wave to reach upto the closed end of a pipe filled with…
In 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
$\frac{1}{3 t}$
$\frac{1}{t}$
$\frac{1}{4 t}$
$\frac{1}{2 t}$
Solution
The distance between the open end and the closed end in the fundamental mode is $\frac{\lambda}{4}$. If the time required to cover the distance is $\mathrm{t}$, then the time required to travel distance equal to $\lambda$ will be $4 \mathrm{t}$. Therefore the period of the wave is $4 \mathrm{t}$. Hence the frequency is $\frac{1}{4 \mathrm{t}}$.
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