Question

A sine function can be used to model light waves. Green light has a wavelength, or period, of about 520 nanometers (nm). Which equation best models green light?

Answer 1

Answer:

$y=\sin\frac{\pi}{260}\theta$

Explanation:

Given:

Period of green light = 520 nm

To find:

A sine equation that best models green light

Note that a sine function is generally given as;

$y=\sin(B\theta)$

And the period(P) of a sine function is given as;

$P=\frac{2\pi}{B}$

Given the period of green light as 520 nm, we can go ahead and solve for B as seen below;

$\begin{gathered} 520=\frac{2\pi}{B} \\ 520B=2\pi \\ \frac{520B}{520}=\frac{2\pi}{520} \\ B=\frac{\pi}{260} \end{gathered}$

Since B = pi/260, we can go ahead and write the equation that models the green light as;

$y=\sin\frac{\pi}{260}\theta$