An electromagnetic wave is traveling upwards along the y-axis, while a second wave is traveling downwards. The electric field in the x-direction and the magnetic field in the z-direction in a certain region in space are described by the following expressions:
Ex = E0 sin(ky - ωt) + E0 sin(ky + ωt)
Bz = B0 sin(ky - ωt) - B0 sin(ky + ωt)
Derive equations that describe the standing wave patterns for the electric field and the magnetic field.
[Hint: sin(A) + sin(B) = 2 sin((A + B) / 2) cos((A - B) / 2)
sin(A) - sin(B) = 2 cos((A + B) / 2) sin((A - B) / 2)]