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

`y=\sin(\pi)/(260)\theta`

Step-by-step 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=(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=(2\pi)/(B) \\ 520B=2\pi \\ (520B)/(520)=(2\pi)/(520) \\ B=(\pi)/(260) \end{gathered}`

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

`y=\sin(\pi)/(260)\theta`