# Chapter 4 - Review Exercises - Page 645: 82

The equation of the blue light wave is $y=\sin \frac{\pi }{240}x$ and that of the red light wave is $y=\sin \frac{\pi }{320}x$.

#### Work Step by Step

Red light wave: We know that this is a sine wave with a period of 640. The amplitude is 1, so $A=1$ Now, B can be calculated as follows: \begin{align} & B=\frac{2\pi }{\text{Period}} \\ & =\frac{2\pi }{640} \\ & =\frac{\pi }{320} \end{align} Thus, model the red light wave as follows: \begin{align} & y=A\sin Bx \\ & y=\sin \frac{\pi }{320}x \end{align} Blue light wave: We know that this is a sine wave with a period of 480. The amplitude is 1, so $A=1$ Now, B can be calculated as follows: \begin{align} & B=\frac{2\pi }{\text{Period}} \\ & =\frac{2\pi }{480} \\ & =\frac{\pi }{240} \end{align} Thus, model the blue light wave as follows: \begin{align} & y=A\sin Bx \\ & y=\sin \frac{\pi }{240}x \end{align}

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