Question

Why does Intensity drop off with (1/r^2) but amplitude drop off with only (1/r)?

Answer 1

intensity isnt like power? the amplitude is proportional to V but power is proportiona to V²

Answer 2

Intensity is usually defined as the square of amplitude

Answer 3

It is usually defined as the square of the amplitude yes, but that tells us that it is also proportional to 1/r^2. The one 1/r^2 comes from the fact that the Area of a sphere is 4pir^2, but i can't see how the amplitude is only 1/r.

Answer 4

If you're fine with intensity having an inverse-square dependence you can just work from that:
\[Intensity \propto \frac{1}{r^2}\]
\[\sqrt{Intensity} \propto\sqrt{\frac{1}{r^2}}\]
\[\therefore Amplitude \propto\frac{1}{r}\]

Answer 5

That's a neat way of looking at it, thank you!