(a) Let S be the sphere of center x and radius R. What is

Chapter 9, Problem 6

(choose chapter or problem)

(a) Let S be the sphere of center x and radius R. What is the surface area of S{|x| < }, the portion of S that lies within the sphere ofcenter 0 and radius ? (b) Solve the wave equation in three dimensions for t > 0 with the initial conditions (x)0,(x)= A for|x| < ,and (x)=0 for|x| >, where A is a constant. Sketch the regions in spacetime that illustrate your answer. (This is like the hammer blow of Section 2.1.) (c) Sketch the graph of the solution (u versus|x|) for t = 1 2,1, and 2, assuming that =c = A =1. (This is a movie of the solution.) (d) Sketchthegraphofuversust for|x|=1 2 and 2,assumingthat =c = A =1. (This is what a stationary observer sees.)(e) Let |x0|