How are a wave's energy and the wave's amplitude related?
Energy is one-half the amplitude
Energy is double the amplitude
Energy is the reciprocal of the amplitude
Energy is proportional to the square of the amplitude is this c?

Question

How are a wave's energy and the wave's amplitude related?
       Energy is one-half the amplitude
       Energy is double the amplitude
       Energy is the reciprocal of the amplitude
       Energy is proportional to the square of the amplitude         is this c?

anonymous · Answer

Energy and amplitude. Amplitude represents the maximum displacement from the equilibrium position. So the larger the amplitude, the larger you'd expect the energy of the wave to be. This would narrow it to B and D.

B means that energy is linear with amplitude: E = 2A
D means that energy is non-linear with amplitude: E = A^2

Energies in physics are based on quadratic variables. So you would consider the energy to be proportional to the amplitude squared, rather than just a linear relationship.

So I would say D should be correct here.