Chapter 35, Problem 50E

(a)

To determine

To show: The resultant wave is given by $E_p\left(t\right)=2E\cos \left(\frac{\varphi }{2}\right)\cos \left(\omega t+\frac{\varphi }{2}\right)$.

(b)

To determine

To show: The amplitude of the resultant wave is given by $2E\cos \left(\frac{\varphi }{2}\right)$.

(c)

To determine

To show: The amplitude of resultant wave is in phase with $E_1$ and $E_2$ have an interference maximum.

(d)

To determine

To show: At interference minimum the resultant wave is out of phase by one by fourth with either of the original waves.

(e)

To determine

To show: The resultant Poynting vector is $4{\epsilon }_{0}c{E}^2{\cos }^2\left(\frac{\varphi }{2}\right){\cos }^2\left(\omega t+\frac{\varphi }{2}\right)$.