- #1
somethingstra
- 17
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Hello, I have some trouble seeing why the solution of the wave equation in 2 dimensions exist at all later times once it passes an initial disturbance...
For example, take a simple case where the initial position is zero, and the initial velocity equals some function inside some circle domain. The solution would be:
\frac{1}{2\pi }\int \int \frac{\psi (x,y)\partial x\partial y}{\sqrt{t_{o}^{2}-(x-x_{0})^{2}-(y-y_{o})^{2}}}
1) Where in that equation tells you that the solutions continues to exist at all later times?
2) If the initial velocity was zero outside the circle domain, why would the solution continue to exist? If we plug in Ψ = 0, wouldn't the solution be zero instead?
3) Can a solution be negative?
For example, take a simple case where the initial position is zero, and the initial velocity equals some function inside some circle domain. The solution would be:
\frac{1}{2\pi }\int \int \frac{\psi (x,y)\partial x\partial y}{\sqrt{t_{o}^{2}-(x-x_{0})^{2}-(y-y_{o})^{2}}}
1) Where in that equation tells you that the solutions continues to exist at all later times?
2) If the initial velocity was zero outside the circle domain, why would the solution continue to exist? If we plug in Ψ = 0, wouldn't the solution be zero instead?
3) Can a solution be negative?
