(Spherically expanding waves) If f is a twice differentiable
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(Spherically expanding waves) If f is a twice differentiable function of one variable and R D px2 C y2 C z2, show that u
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(Spherically expanding waves) If f is a twice differentiable function of one variable and R D px2 C y2 C z2, show that u.x; y; z; t / D f .R ? ct/ R satisfies the three-dimensional wave equation @2u @t2 D c2 @2u @x2 C @2u @y2 C @2u @z2 : What is the geometric significance of this solution as a function of increasing time t? Hint: You may want to use the result of Exercise 3. In this case v.R; ; / is independent of and .
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