The displacement of a particle on a stretched string is given by
y(x,t)=0.040msin(180x−5400t),
where x and y are in metres and t in seconds.
(a) Obtain expressions for the particle velocity vp(x,t) and particle acceleration ap(x,t) as functions of x and t.
(b) Calculate the maximum particle velocity and the maximum particle acceleration for this wave.
(c) Show that the ratio of the maximum particle acceleration to the maximum particle velocity equals the angular frequency of the wave.