Why is wave energy proportional to amplitude squared?

[teodorakis]

http://www.schoolphysics.co.uk/age1...rties/text/Intensity_and_amplitude/index.html
well this may be alittle bit simple but in the link above the energy of a physical wave is shown as squared i mean is this done to eliminate that the positive and negative values cancel each other?

 

[Pierce610]

If you have a sinusoid as voltage and R, so the phase between Voltage and current is zero.
Then also I is sinusoidal.
The power P = V x I = V sin t x I sin t = VI sin^2 t.

 

[blue_leaf77]

The energy of a physical system always accounts for the total energy, that is the sum of (total) kinetic energy and (total) potential energy. Kinetic energy is proportional to square of velocity. For a system that can be modeled as a vibrating spring (which is perhaps true for all sinusoidal dynamic system), the potential energy is proportional to square of displacement. That's the total energy must be proportional to square of its amplitude.

 

[blue_leaf77]

I guess you are the type of "yellow card" collector Adam. I'm not sure if there is a maximum limit of the number collected.