# Chapter 14 - Exercises and Problems - Page 272: 55

The proof is below.

#### Work Step by Step

We find: $=Acos(kx-\omega t )+ Acos(kx-\omega t +\phi/2)$ Using trigonometry, we can simplify this to: $=2A cos(kx-\omega t +\phi/2)$. Thus, from the inside of the cosine function, we see that the wave is a simple harmonic wave. The amplitude is 2A, but the book wants this in terms of the phase constant, so we find that the amplitude is $2Acos(\phi/2)$

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