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?
1. y = sin 260/pi theta
2. y = sin pi/520 theta
3. y = sin 520/pi theta
4. y = sin pi/260 theta
y = sin pi/260 theta , depending on what "theta" is.
A sine function can be used to model light waves. Green light has a wavelength, or period, of about 530 nanometers (nm). Which equation best models green light?
y=sin pi/265 theta
y= sin pi/530 theta
y= sin 530/pi theta
y= sin 265/pi theta
A sine function can be used to model light waves. Green light has a wave length, or period of about 520 nm. Which equation best models green light?
A.) y=sin 260/pi theta
B.) y= sin pi/520 theta
C.) y= sin 520/pi theta
D.) y= sin pi/260 theta
B.) y= sin pi/520 theta is the equation that best models green light.
Well, let me brighten up this question with some humor!
Green light is pretty chill, always keeping things balanced. So, I'd say option 2 - y = sin(pi/520) theta - best models green light. After all, it's all about finding the right wavelength... and the right punchline!
To determine which equation best models green light, we need to consider the properties of a sine function and the given wavelength or period of green light.
The general equation for a sine function is y = A * sin(B * theta + C), where A represents the amplitude, B represents the frequency, and C represents the phase shift.
In the given options, we have:
1. y = sin 260/pi theta
2. y = sin pi/520 theta
3. y = sin 520/pi theta
4. y = sin pi/260 theta
Here, theta represents the variable for the angle, and the numbers outside the sine function denote the constants involved.
The wavelength or period is given as 520 nanometers (nm). The period of a sine function is the length of one complete cycle. In this case, the period of green light is 520 nm.
The formula to calculate the wavelength from the period is λ = 2π / B, where λ represents the wavelength and B represents the frequency. In our case, we know the period (520 nm) and need to find the frequency or B.
First, let's convert the wavelength from nm to radians:
λ = 520 nm = 520 * 10^(-9) m = 520 * 10^(-9) / (2π) radians
Now, to have the correct B value, we need to represent the wavelength as 2π / B:
520 * 10^(-9) / (2π) = 2π / B
By cross-multiplying and solving for B, we get:
B = 2π / (520 * 10^(-9))
Since the correct B value involves calculating the reciprocal of the wavelength, we can rule out options 1 and 3.
Now, let's analyze the remaining options:
2. y = sin pi/520 theta
4. y = sin pi/260 theta
Comparing these options, we can conclude that option 2 is the correct choice because it represents the correct B value. Therefore, the equation that best models green light is y = sin(pi/520 * theta).