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Unformatted text preview: Physics 505 Fall 2007 Homework Assignment #10 — Due Thursday, November 29 Textbook problems: Ch. 6: 6.1, 6.4, 6.13, 6.18 6.1 In three dimensions the solution to the wave equation (6.32) for a point source in space and time (a light flash at t = 0 ,~x = 0) is a spherical shell disturbance of radius R = ct , namely the Green function G (+) (6.44). It may be initially surprising that in one or two dimensions, the disturbance possesses a “wake”, even though the source is a “point” in space and time. The solutions for fewer dimensions than three can be found by superposition in the superfluous dimension(s), to eliminate dependence on such variable(s). For example, a flashing line source of uniform amplitude is equivalent to a point source in two dimensions. a ) Starting with the retarded solution to the three-dimensional wave equation (6.47), show that the source f ( ~x ,t ) = δ ( x ) δ ( y ) δ ( t ), equivalent to a t = 0 point source at the origin in two spatial dimensions, produces a two-dimensional wave Ψ( x,y,t ) = 2 c Θ( ct- ρ ) p c 2 t 2- ρ 2 where ρ 2 = x 2...
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