Problems on Light as a wave
Problem 1.1:
Find an expression for the angular frequency of a wave in terms of the wavelength and phase
velocity.
[Solution]
Problem 1.2:
If the numbers in this problem are given in SI units, calculate the velocity of a wave given by the equation:
ψ(y, t) = (9.3×104)sin[π(9.7×106y + 1.2×1015t)].
[Solution]
Problem 1.3:
Write the equation for a wave with an amplitude
2.5×103 V/m, a period
4.4×10-15 seconds, and speed
3.0×108 m/s, which is propagating in the negative
z-direction
with value
2.5×103 V/m at
t = 0,
z = 0.
[Solution]
Problem 1.4:
Consider the wave
ψ(x, t) = A cos(k(x + vt) + π). Find an expression (in terms of A) for the
magnitude of the wave when
x = 0,
t = T/2, and
x = 0,
t = 3T/4 .
[Solution]
Problem 1.5:
Demonstrate explicitly that a harmonic function
ψ(x, t) = A cos(kx - ωt) satisfies the wave
equation. What condition needs to be fulfilled?
[Solution]
