What is a wave? The one-dimensional wave equation

2/3/14Waves as rotating vectorsWaves using complex numbersE = E 0cos k(x − ct);φ = k(x − ct)The argument of the cosine function represents the phase of the wave,ϕ, or the fraction of a complete cycle of the wave.€Using complex numbers, we can write the harmonic wave equation as:E = E 0e ik(x −ct ) = E 0e i(kx−ωt )i.e., E = E 0 cos(ϕ) + i E 0 sin(ϕ), where the ‘real’ part of the expressionactually represents the wave.€We also need to specify the displacement E at x = 0 and t = 0, i.e., the‘initial’ displacement.7