What is a wave? The one-dimensional wave equation

2/3/14Amplitude and Absolute phaseE(x,t) = A cos[(k x – ω t ) – θ ]A = Amplitudeθ = Absolute phase (or initial, constant phase) at x = 0, t =0π kxWaves using complex numbersSo the electric field of an EM wave can be written:E(x,t) = E 0 cos(kx – ωt – θ)Since exp(iϕ) = cos(ϕ) + i sin(ϕ), E(x,t) can also be written:E(x,t) = Re { E 0 exp[i(kx – ωt – θ)] }Recall that the energy transferred by a wave (flux density) isproportional to the square of the amplitude, i.e., E 02 . Only theinteraction of the wave with matter can alter the energy of thepropagating wave.Remote sensing exploits this modulation of energy.8