Sinusoidal Waves.

We shift our attention to oscillations that propagate in space as time evolves. This is referred to as a wave. The sinusoidal wave

$$a(x,t)=A \, \cos(\omega t - k x+ \psi)$$ (6.1)

is the simplest example of a wave, we shall consider other possibilities later in the course. It is often convenient to represent the wave in the complex notation introduced earlier. We have

$$\tilde{a}(x,t)=\tilde{A}\, e^{i(\omega t - k x)}$$ (6.2)