Chapter 7.2, Problem 21P

Write the equation for a sinusoidal wave of wavelength 4, amplitude 20, and velocity 6. (See Problem 17.) Make computer plots of y as a function of $t$ for $x=0,1,$

2,3, and of $y$ as a function of $x$ for $t=0,\frac{1}{6},\frac{1}{3},\frac{1}{2}.$ If this wave represents the shape of a long rope which is being shaken back and forth at one end, find the velocity $\partial y/\partial t$ of particles of the rope as a function of $x$ and t. (Note that this velocity has nothing to do with the wave velocity v, which is the rate at which crest of the wave move forward.)