What is the relationship between intensity and amplitude in a wave source?

[Gauss M.D.]

This is something I don't relly get. I keep reading that the intensity of a wave is proportional to the square of its amplitude.

So let's suppose we have a random wave source, with amplitude A₀. If we replace that source with five identical copies of it, their collective amplitude is 5A, yes? But have I really raised the energy level at the source by a factor of 25? What am I missing here?

 

[TSny]

If we replace that source with five identical copies of it, their collective amplitude is 5A, yes? But have I really raised the energy level at the source by a factor of 25? What am I missing here?

Are you assuming that the 5 identical sources are located in exactly the same spot (superimposed on one another)? If so, then I believe the total energy radiated by the sources would be 25 times greater than one source alone.

Think about the special case where the source is just a single charge q oscillating in simple harmonic motion . Superimposing 5 such oscillators is simply equivalent to increasing the charge from q to 5q. The power radiated by an oscillating charge is proportional to the square of the charge. So, the energy radiated with 5q is 25 times that of q.

If the 5 oscillators do not oscillate in phase, but have randomly changing phase shifts relative to one another, then I believe the average radiated power output would be just 5 times that of one oscillator.

 

[Drakkith]

How do intensity, amplitude, and power all relate to each other in this context?