Question

If the frequency of the wave is 100 Hz then the particles of the medium cross the mean position in 1 s will be
A. 50 times
B. 100 times
C. 200 times
D. 400 times

Answer 1

The frequency is nothing but the number of oscillations in one second. OR. The number of waves that pass a fixed point in a given amount of time is called the frequency. The mean position of a wave is the horizontal line around which it oscillates while carrying energy.

Complete answer:
Considering that a wave starts to oscillate from the point of origin, thus, one complete oscillation crosses the mean position 2 times.
The wave oscillation diagram is:

The above figure represents the number of times the wave crosses the mean position in one oscillation.
The point of origin should not be considered as the wave starts to oscillate from that point.

$100\,Hz$ refers to the 100 oscillations.
As for $1$ oscillation, the wave crosses the mean position $2$ times, thus, for $100$ oscillations, the wave crosses the mean position $2\times 100=200$ times.
The number of times the particles of the medium cross the mean position in$1\,s$ will be $200$ times.

As the number of times the particles of the medium cross the mean position in $1\,s$ will be $200$ times.

So, the correct answer is “Option C”.

Note:
The things to be on your figure tips for further information on solving these types of problems are:
While counting for the number of times the mean position is crossed by the wave, the point of origin should not be taken into consideration, as the motion starts from that point itself.