Question 467: Waves

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

Accepted Answer

In the case of a fundamental mode, the time required for a sound wave to travel to the closed end of a pipe filled with air is denoted as ' $t$ ' seconds. The frequency of vibration of the air column can be calculated as follows:
For a closed organ pipe, the fundamental frequency is expressed by the formula:
$ f_0 = \frac{v}{4L} \quad 	ext{.... (i)} $
where:
$ v $ is the velocity of the sound wave inside the pipe.
$ L $ is the length of the pipe.
Given that the time taken for the wave to reach the other end is $ t $ seconds, we can relate this to the length of the pipe with the equation:
$ t = \frac{L}{v} \quad 	ext{.... (ii)} $
Substitute equation (ii) into equation (i):
$ f_0 = \frac{1}{4} \cdot \frac{1}{t} = (4t)^{-1} $
Thus, the frequency of vibration of the air column is $(4t)^{-1}$.

Answer

$(2 t)^{-1}$

Answer

$4(t)^{-1}$

Answer

$2(t)^{-1}$

Answer

$(4 t)^{-1}$

Waves

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

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