Question

A sine function can be used to model light waves. Green light has a wave length, or period of about 510 nm . which equation best models green light? a. y= sin pi/510 theta b. y= sin pi/255 theta c. y= sin 510/pi theta d. sin 255/pi theta

Answer 1

A sine function can be used to model light waves. Green light has a wave length, or period of about 510 nm. The equation that best models green light is y= sin 510/pi theta. The answer is letter C.

Answer 2

`y=\sin((\pi \theta)/(255))`

B is correct.

Explanation:

A sine function can be used to model light waves. Green light has a wave length, or period of about 510 nm .

Equation of sine wave:

`y=\sin(ax)`

As we know the period of sine function is 2π

Period of this function
`y=\sin(ax)` is 2π/a

We are given the period of function is 510

Thus,
`510=(2\pi)/(a)`

Now we will solve for a

`a=(2\pi)/(510)`

`a=(\pi)/(255)`

Required equation:
`y=\sin((\pi \theta)/(255))`

Hence, The equation for best models green light is
`y=\sin((\pi \theta)/(255))`