Ripples radiate outward on the surface of a shallow pond after a stone is dropped at the point x=0. At time t=0, the point x=1.5m experiences the passage of a crest moving in the +x direction. The water at that point then returns to equilibrium 0.40s later. The wave speed on the pond is measured to be 2.1ms−1, and the vertical distance from a crest to trough is 0.50cm.
(a) Determine the period and frequency of the wave at x=1.5m. Show your reasoning.
(b) Calculate the wavelength.
(c) Write an explicit equation y(x,t) for the vertical displacement of the water surface for x>0, choosing coordinates so that x=0 is the point where the stone was dropped and t=0 is defined above. Take upward displacement as positive.
(d) Using your equation, find the earliest time after t=0 at which the point x=4.5m is at maximum negative displacement.