Answer
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:
$\begin{align}
& y=A\sin Bx \\
& y=\sin \frac{\pi }{240}x
\end{align}$
