Question

How does frequency of vibrations of small objects floating in water compare to the number of waves passing it each second?

Answer 1

Hint: The number of waves passing through a small object each second gives the number of times the object moves up and down in the same position. It also defines the frequency of vibration of a small object floating in water. Frequency and time periods are dependent on each other so it also defines the time period of vibrating small objects.

Complete step-by-step solution:
In this question we have to compare the frequency of oscillating object in water to the number of waves passing each second for that purpose we should assume that we have kept a small object on the surface of the water and initially water and the small object both are at rest.If we create a some disturbance anywhere in the water by throwing a small stone in water then ripples will be formed as the waves on the surface of water and water start oscillating up and down about its mean position, these oscillations are transverse in nature and small object will also experience same type of oscillation so it starts oscillating up and down in similar way as the motion of water molecules is performed because it is residing inside the medium. Since the small object will also experience an up and down motion as the vibrations then the time period of this up and down motion of the small object will be similar to the time period of waves generated on the water surface. Since the time periods of vibrations of water and time period that of oscillating small objects are same then the frequency of the waves formed in water and the frequency of vibration of the small object will also be same because time period and frequency of vibrations are dependent on each other.
So we conclude that the number of waves passing the small object in each second and the frequency of its vibration of water will be the same.

Note: No of oscillations completed in one second is called its frequency .In one oscillations particle moves up and down one time and time taken to complete this one oscillation is called its time period. This Time period and frequency are inversely connected to each other. Number of waves passing through a small object gives the number of times the object moves up and down.