16.5 Exercise 17

Consider two wave functions that differ only by a phase shift, $y_{1} \left(x , t\right) = A \text{cos} \left(k x - \omega t\right)$ and $y_{2} \left(x , t\right) = A \text{cos} \left(k x - \omega t + \phi\right) .$ Use the trigonometric identities $\text{cos} u + \text{cos} v = 2 \text{cos} \left(\frac{u - v}{2}\right) \text{cos} \left(\frac{u + v}{2}\right)$ and $\text{cos} \left(− \theta\right) = \text{cos} \left(\theta\right)$ to find a wave equation for the wave resulting from the superposition of the two waves. Does the resulting wave function come as a surprise to you?