Ocean swells move toward the shore along the direction

PHYSICS · Multi-part · A Level · Physics · Waves · Waves

Problem

Ocean swells move toward the shore along the

+x

direction. At a dock located at

x=0

, a sensor records that the water surface passes through its equilibrium position moving upward at time

t=0

. Measurements show that successive crests pass the dock every

7.5\,\text{s}

and the vertical distance from a crest to the equilibrium level is

0.80\,\text{m}

. The horizontal distance between successive crests is

12\,\text{m}

. (a) Determine the wave’s amplitude, frequency, and wavelength. State appropriate units. (b) Write an explicit equation

y(x,t)

for the vertical displacement of the water surface as a function of horizontal position

x

and time

t

. Take upward displacement as positive. (c) Using your equation, calculate the vertical displacement of the water surface at the point

x=4.0\,\text{m}

at time

t=18\,\text{s}

. Include the sign of the displacement.