phase

1. Physics 101-Learning Object
Phase and Phase Difference

2. Phase
• The wave function of a harmonic wave can be written as:
D(x,t) = Asin (kx-ωt+ɸ) when it is travelling in the direction of
increasing x (position along the string) , and can be written as
D(x,t) = Asin (kx+ωt+ɸ) when it is travelling in the direction of
decreasing x.
• The phase of a harmonic wave is designated by the Greek letter phi, ɸ
and is measured in radians. The phase, which is dependent on
position and time, is the fraction of the wave cycle that has passed by
with respect to the origin.
• The phase is the expression inside the brackets of the wave function
of a harmonic wave (x,t), therefore the phase can be written as:
ɸ (x,t) = kx+ωt+ɸ
• NOTE: DO NOT CONFUSE PHASE, ɸ, WITH PHASE CONSTANT, ɸ.

3. Phase Difference
• The phase difference of a harmonic wave is designated by Δɸ
and is measured in radians. The phase difference is the
difference between the phase at two separate points (x₁ and
x₂), at the same time. Therefore:
Δɸ = phase of wave at x₂ - phase if wave at x₁
= (kx₂-ωt+ɸ) - (kx₁-ωt+ɸ)
= k (x₂ - x₁)
= kΔx = 2π(Δx/λ), where λ is the wavelength

4. Practice Questions
• The wave function of a harmonic wave is given by the function
D(x,t) = (0.5m)sin (4x-2t+(π/2)),
1) what is the expression for the phase of this wave?
2) what is the phase when t=3sec and x=2m?
3) if the difference between two points is λ/6, what is the
phase difference?

5. Solutions
• Answers:
1) Phase = 4x-2t+(π/2)
2) Phase = 4(2)-2(3)+(π/2) = 3.57 rad
3) Phase difference = 2π(Δx/λ) = 2π((λ/6)/λ) = π/3