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In this problem we will consider combining electromagnetic waves with different po- larization states. In the first two parts of this problem, we will consider two electromagnetic waves transmitted by two different satellites. These two waves have the same frequency and can be represented by the phasors: E₁(y) = E(2³/6 – 32e³4x/6)e-jky E₂(y) = E(î - 32e¯jx/3) e-jky In the above, E01 and E02 are real constants. (a) In what direction do the waves corresponding to E₁(y) and E2(y) travel? (b) What is the polarization state of the wave corresponding to E₁(y)? (c) You are told that the time-average power densities of the two waves are the same. Find the polarization state of the wave that results from their combination, that is, the wave corresponding to E₁(y) + E2(y).

In this problem we will consider combining electromagnetic waves with different po- larization states. In the first two parts of this problem, we will consider two electromagnetic waves transmitted by two different satellites. These two waves have the same frequency and can be represented by the phasors: E₁(y) = E(2³/6 – 32e³4x/6)e-jky E₂(y) = E(î - 32e¯jx/3) e-jky In the above, E01 and E02 are real constants. (a) In what direction do the waves corresponding to E₁(y) and E2(y) travel? (b) What is the polarization state of the wave corresponding to E₁(y)? (c) You are told that the time-average power densities of the two waves are the same. Find the polarization state of the wave that results from their combination, that is, the wave corresponding to E₁(y) + E2(y).

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please help me in any way you can. I dont understand EM waves.

 

In this problem we will consider combining electromagnetic waves with different po- larization states. In the first two parts of this problem, we will consider two electromagnetic waves transmitted by two different satellites. These two waves have the same frequency and can be represented by the phasors: E₁(y)=E(e/6-32e³4x/6)e-jky E₂(y) = E0₂(2-32e-jx/³) e-jky In the above, E01 and E02 are real constants. (a) In what direction do the waves corresponding to E₁(y) and E2(y) travel? (b) What is the polarization state of the wave corresponding to E₁(y)? (c) You are told that the time-average power densities of the two waves are the same. Find the polarization state of the wave that results from their combination, that is, the wave corresponding to E₁(y) + E2(y). In the next two parts of this problem, let's consider other combinations of waves with differing polarization states. For the following parts, you may assume that all of the waves travel in the +z-direction. (d) Consider combining a right-hand circularly polarized wave of amplitude a/2 with a left-hand circularly polarized wave of amplitude a/2. What is the polarization state and amplitude of the combined wave? (e) Consider combining a right-hand circularly polarized wave of amplitude (+¹) with a left-hand circularly polarized wave of amplitude (E-E¹). What is the po- larization state of the combined wave? Are there any interesting physical implications of this result?
Transcribed Image Text:In this problem we will consider combining electromagnetic waves with different po- larization states. In the first two parts of this problem, we will consider two electromagnetic waves transmitted by two different satellites. These two waves have the same frequency and can be represented by the phasors: E₁(y)=E(e/6-32e³4x/6)e-jky E₂(y) = E0₂(2-32e-jx/³) e-jky In the above, E01 and E02 are real constants. (a) In what direction do the waves corresponding to E₁(y) and E2(y) travel? (b) What is the polarization state of the wave corresponding to E₁(y)? (c) You are told that the time-average power densities of the two waves are the same. Find the polarization state of the wave that results from their combination, that is, the wave corresponding to E₁(y) + E2(y). In the next two parts of this problem, let's consider other combinations of waves with differing polarization states. For the following parts, you may assume that all of the waves travel in the +z-direction. (d) Consider combining a right-hand circularly polarized wave of amplitude a/2 with a left-hand circularly polarized wave of amplitude a/2. What is the polarization state and amplitude of the combined wave? (e) Consider combining a right-hand circularly polarized wave of amplitude (+¹) with a left-hand circularly polarized wave of amplitude (E-E¹). What is the po- larization state of the combined wave? Are there any interesting physical implications of this result?
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