Changes

Calculation of g proves more challenging. We know the wave equation

Calculation of g proves more challenging. We know the wave equation

<math>\frac{d^2y}{dt^2} - \frac{c^2d^2y}{dx^2} = 0</math>

<math>\frac{d^2y}{dt^2} - c^2\frac{d^2y}{dx^2} = 0</math>

However, this is for a uniform, sourceless wave. Like most generalizations, this is an unrealistic situation in the real world. What we need is a function that can generate a brief pulse. This sounds like a delta function.

However, this is for a uniform, sourceless wave. Like most generalizations, this is an unrealistic situation in the real world. What we need is a function that can generate a brief pulse. This sounds like a delta function.

<math>\frac{d^2g}{dt^2} - \frac{c^2d^2g}{dx^2} = \delta(\Delta \mathbf{x})\delta(\Delta t)</math>

<math>\frac{d^2g}{dt^2} - c^2\frac{d^2g}{dx^2} = \delta^3(\Delta \mathbf{x})\delta(\Delta t)</math>

This is not an easy equation to solve without using a Fourier transform. Therefore, we'll do just that, with G as the transformed function.

This is not an easy equation to solve without using a Fourier transform. Therefore, we'll do just that, with G as the transformed function.