Phase constant for light waves

In summary, the problem is asking to find the sum of two waves, E_1 and E_2, with given functions. To solve this, we can use the equation E_1 + E_2 = Asin(100 \pi t + B) and compare coefficients to find the values of A and B. We can also use the sine addition formula to simplify E_2. More guidance can be found in the provided link on linear combinations.
  • #1
roam
1,271
12

Homework Statement



We have two waves with functions:

[tex]E_1 = 6 \ sin (100 \pi t)[/tex]

[tex]E_2 = 8 \ sin (100 \pi t + \frac{\pi}{2})[/tex]

Find [tex]E_1 + E_2[/tex].

Homework Equations



[tex]\phi = \frac{2 \pi}{\lambda} \delta = \frac{2 \pi}{\lambda} d sin \theta[/tex]

[tex]\frac{\delta}{\lambda}=\frac{\phi}{2 \pi}[/tex]

The Attempt at a Solution



The answer to this problem should be [tex]10 \ sin (100 \pi t + 0.927)[/tex]
I can't understand how they got the value for the phase constant phi to be 0.927. I can't understand how they got the value using the above equations... because we don't know and can't find many variables in those equations. And I'm not sure how to use trig fro this... Any help with this problem is greatly appreciated.
 
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  • #2
Let

[itex]E_1 + E_2 = Asin(100 \pi t + B)[/itex]

Use this and compare coefficients to get the values of A and B. You might want to use the sine addition formula on [itex]E_2[/itex] to first simplify that expression.
 
  • #3
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What is the phase constant for light waves?

The phase constant for light waves is a measure of the initial phase of a light wave. It represents the position of the wave at the beginning of its cycle.

How is the phase constant for light waves related to wavelength?

The phase constant for light waves is directly related to the wavelength of the wave. A longer wavelength corresponds to a larger phase constant, while a shorter wavelength corresponds to a smaller phase constant.

What is the significance of the phase constant in light wave interference?

The phase constant plays a crucial role in light wave interference. It determines whether two waves will constructively or destructively interfere with each other, and thus affects the resulting intensity of the light.

How does the phase constant change when light waves travel through different mediums?

The phase constant remains constant when light waves travel through a vacuum. However, it can change when the waves travel through different mediums with varying refractive indices. This is known as phase shift.

Can the phase constant for light waves be negative?

Yes, the phase constant for light waves can be negative. This indicates that the wave begins at a point that is shifted in the opposite direction from the origin, compared to a positive phase constant where the wave begins at the origin.

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