16.6 Exercise 40

Consider two periodic wave functions, $y_{1} \left(x , t\right) = A \text{sin} \left(k x - \omega t\right)$ and $y_{2} \left(x , t\right) = A \text{sin} \left(k x - \omega t + \phi\right) .$ (a) For what values of $\phi$ will the wave that results from a superposition of the wave functions have an amplitude of 2A? (b) For what values of $\phi$ will the wave that results from a superposition of the wave functions have an amplitude of zero?