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Full-Text Articles in Physics
07 General Solution Of The One-Dimensional Wave Equation, Charles G. Torre
07 General Solution Of The One-Dimensional Wave Equation, Charles G. Torre
Foundations of Wave Phenomena
We will now find the “general solution” to the one-dimensional wave equation (5.11). What this means is that we will find a formula involving some “data” — some arbitrary functions — which provides every possible solution to the wave equation.
09 The Wave Equation In 3 Dimensions, Charles G. Torre
09 The Wave Equation In 3 Dimensions, Charles G. Torre
Foundations of Wave Phenomena
We now turn to the 3-dimensional version of the wave equation, which can be used to describe a variety of wavelike phenomena, e.g., sound waves and electromagnetic waves. One could derive this version of the wave equation much as we did the one-dimensional version by generalizing our line of coupled oscillators to a 3-dimensional array of oscillators. For many purposes, e.g., modeling propagation of sound, this provides a useful discrete model of a three dimensional solid.