Question

The time lag between two particles vibrating in a progressive wave separated by a distance 20 m is 0.02 sec. The wave velocity if the frequency of the wave is 500 Hz is:

A. $1000\,m{s^{ - 1}}$

B. $500\,m{s^{ - 1}}$

C. $2000\,m{s^{ - 1}}$

D. $250\,m{s^{ - 1}}$

Answer 1

Vibration is defined as the forward and backward motion from its equilibrium position of the particles. Frequency is defined as the number of the oscillations in one second the S.I unit of the frequency is Hertz.

Formula used: The formula of the speed is given by,

$s = \dfrac{d}{t}$

Where speed is s, the distance is d and the time taken is t.

Complete step by step answer:

It is given in the problem that the time lag between two particles vibrating in a progressive wave separated by a distance 20 m is 0.02sec. The frequency of the wave is 500 Hz then we need to find the velocity of the wave. The distance between the two particles is 20 m and the time taken by the wave to travel to this distance is 0.02 sec.

The formula of the speed is given by,

$s = \dfrac{d}{t}$

Where speed is s, the distance is d and the time taken is t.

The distance between the two particles is 20 m and the time taken is 0.02 sec. the speed of the wave is equal to,

$\Rightarrow s = \dfrac{d}{t}$

$\Rightarrow s = \dfrac{{20}}{{0 \cdot 02}}$

$\Rightarrow s = 1000\,m{s^{ - 1}}$.

The speed of the wave is equal to $s = 1000\,m{s^{ - 1}}$.

The correct answer for this problem is option A.

Note: The sound energy is transferred by the help of vibration and the particles transfer the energy in the atmosphere by the vibrating and passing the energy to the next particle as it is given that the two particles are separated by the distance 20 m and the vibration happens after 0.02 sec. which means that the energy is transferred to the other particle in 0.02 seconds which is 20 m away.