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Re: [Phys-L] definition of "wave"



Take the one dimensional wave equation to be:

d^2 f(x,t)/dx^2 = (1/v^2)*d^2 f(x,t)/dt^2 (1)

Where "d ()" is the partial differentiation operator.

Let f(x,t) =a*( x^2 + v^2*t^2) where a is a constant which provides the
correct dimensions for the disturbance of interest.


Wow, that’s really intriguing.

If I let time be imaginary and set a=1 we can rewrite f as x^2 - v^2*t^2 = (x+vt)(x-vt) and that looks more promising.

However, I remain puzzled about why these solutions don’t appear to come out of separation of variables when I set f = X(x)*T(t). Setting the separation constant as -k, I can get linear terms (such as x+vt) for k=0, but I don’t see how to get quadratic terms. Obviously I’d be happier with x^2 + 2vxt + v^2*t^2.

Who can help me here?

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Carl E. Mungan, Professor of Physics 410-293-6680 (O) -3729 (F)
Naval Academy Stop 9b, 572C Holloway Rd, Annapolis MD 21402-1363
mailto:mungan@usna.edu http://usna.edu/Users/physics/mungan/