16.6 Exercise 52

Consider two wave functions $y_{1} \left(x , t\right) = A \text{sin} \left(k x - \omega t\right)$ and $y_{2} \left(x , t\right) = A \text{sin} \left(k x + \omega t + \phi\right)$. What is the wave function resulting from the interference of the two wave? (Hint: $\text{sin} \left(\alpha \pm \beta\right) = \text{sin} \alpha \text{cos} \beta \pm \text{cos} \alpha \text{sin} \beta$ and $\phi = \frac{\phi}{2} + \frac{\phi}{2}$.)