《 SECTION 15.2 introduced the concept of phase for an oscillator in simple harmonic motion. Phase is also important for waves. The phase of a sinusoidal wave, denoted $\varphi$, is the quantity $(kx-\omega t+{\varphi }_0)$. Phase will be an important concept in Chapter 17, where we will explore the consequences of adding various waves together. For now, we can note that the wave fronts seen in Figures 16.25 and 16.26 are “surfaces of constant phase.” To see this, write the displacement as simply $D\left(x\text{,\hspace{0.17em}}t\right)=A\text{sin}\varphi$. Because each point on a wave front has the same displacement, the phase must be the same at every point.

It will be useful to know the phase difference $\text{Δ}\varphi$ between two different points on a sinusoidal wave. FIGURE 16.27 shows two points on a sinusoidal wave at time t. The phase difference between these points is

That is, the phase difference between two points on a wave depends on only the ratio of their separation $\text{Δ}x$ to the wavelength $\text{λ}$. For example, two points on a wave separated by $\text{Δ}x=\frac{1}{2}\text{λ}$ have a phase difference $\text{Δ}\varphi =\pi \text{rad}$.

FIGURE 16.27 The phase difference between two points on a wave.

An important consequence of Equation 16.56 is that the phase difference between two adjacent wave fronts is $\mathbf{\text{Δ}}\mathit{\varphi }\mathbf{=}\mathbf{2}\mathit{\pi }\mathbf{\text{rad}}$. This follows from the fact that two adjacent wave fronts are separated by $\text{Δ}x=\text{λ}$. This is an important idea. Moving from one crest of the wave to the next corresponds to changing the distance by $\text{λ}$ and changing the phase by $2\pi \text{rad}$.