A surface wave on still water propagates in the negative x-direction. The amplitude of the surface displacement is 5.0 mm and the frequency of the wave is 2.0 Hz. At t=0, the point on the surface at x=0 has zero displacement and is moving downward. The displacement is to be represented with a cosine function.
(i) If the speed of these waves on the water surface is 1.2 m s−1, determine the wavelength.
(ii) Write the expression for the surface displacement η(x,t) (in millimetres) as a cosine function that satisfies all the conditions given.
(iii) Using your expression, calculate the instantaneous velocity of the surface particle at x=0 at time t=0.40s."