To determine the amplitude of the wave, we need to use the given information that the small cork rises up and down through one complete oscillation every 4 seconds.
The time period (T) of a wave is the time it takes for one complete oscillation. In this case, the time period is given as 4 seconds.
The frequency (f) of a wave is the reciprocal of the time period, so we can calculate the frequency as:
f = 1 / T
f = 1 / 4 = 0.25 Hz
The frequency represents the number of complete oscillations per unit of time.
In the case of a transverse wave, the amplitude (A) refers to the maximum displacement of the particle from its equilibrium position. In this case, the cork rises up and down through one complete oscillation, which means the displacement is from the equilibrium position to the maximum height and back to the equilibrium position.
Since the cork undergoes one complete oscillation during the time period of 4 seconds, we can consider this as one full wave cycle. Therefore, the amplitude (A) is equal to half the distance between the equilibrium position and the maximum height.
Thus, the amplitude of the wave is given by:
A = 1/2 * Maximum Displacement
Since the cork rises up and down through one complete oscillation, the maximum displacement is the distance from the equilibrium position to the maximum height.
Hence, to find the amplitude, we need additional information about the distance or height of the cork's maximum displacement in relation to the equilibrium position.