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 ________.

Options

• (2t)^-1

• 4(t)^-1

• 2(t)^-1

• (4t)^-1

Answer 1

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 (4t)^-1.

Explanation:

As we know, the fundamental frequency for a closed organ pipe is given as,

`"f"_0 = "v"/(4"l")`    ...(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 sac,

As, `"t" = l/"v"`   ...(ii)

Hence, from Eqs. (i) and (ii), we get

`"f"_0 = 1/4 * 1/"t" = (4"t")^(-1)`

So, frequency of vibration of air column is (4t)^-1.