Electromagnetic radiation (for example, light) has two components, an electric field and a magnetic field, which oscillate as the radiation propagates. The electrical field, E(t), can be described by E(t) = Acos(ωt + φ(t)), where A is the amplitude (with units of V m−1 or N C−1 ), ω is the angular frequency (with units of s−1 ), t is time (with units of s) and φ(t) is called the phase function, and is dimensionless.

a. What are the maximum and minimum values of E? Are they affected by φ or ω?

b. Set A = 1 V m−1 and ω = 0.5 s

−1

. Plot E(t) for φ(t) = 0,

φ(t) = 1, φ(t) = t and φ(t) = t 2

. What is the phase function doing?

c. Let E(t) = 2 cos(ω1t)+cos(ω2t) V m−1

, where ω1 = 1 s

−1 and ω2 = 2 s

−1

. Calculate the values of E(t) for t/s = 0,

π

4

,

π

2

, 3π

4

, π, 5π

4

, 3π

2

, and 2π. Sketch (by hand) how you think the function might look. Plot the function properly (using whatever software you want) and compare to your sketch.