Phase corresponds to the position and time on a wave function. Phase difference is the difference between the phases of two waves at the same time. For example, if one wave is at a phase of pi/2 and another is at 0, their phase difference is pi/2. This phase difference describes the offset between the two waves. For periodic waves, the phase difference is set due to the periodic nature of the waves.

1. PHASE & PHASE DIFFERENCE
PHYS 101 LEARNING OBJECTS

2. PHASE ( )
• corresponds to the position and time on the wave
function
• based on the above example of a wave function, points 1, 2, 3, 4 and 5 can be referred
as 0, pi/2, pi, 3pi/2 and 2pi when thinking in respect of the phase of this wave
• labelling of 0, pi/2, pi, 3pi/2 and 2pi are arbitrary may be labelled along different points
of wave (as long as its indicates accurate position of wave at specific time)

3. PHASE DIFFERENCE
• “difference between the phase at 2 points, at the
same time”
• when blue wave is at pi/2, red wave is at 0 phase ; when
blue wave is at pi, red wave is at pi/2 phase (etc.)
• can describe this offset between 2 waves as the phase
difference

4. • in this case: difference of pi/2 in the phase
• the blue wave is always to the left of the red wave by
pi/2
• if these waves are traveling to the left, blue wave is
leading red wave by pi/2 of phase
• if waves traveling to the right, blue wave is trailing
from the red wave by pi/2 of phase

5. EQUATION FOR THE PHASE
DIFFERENCE IN HARMONIC WAVES

6. PHASE DIFFERENCES FOR A
PERIODIC WAVE
• for a periodic wave, the difference in phase is set due to its periodic nature
• the following table will be useful when determining phase difference of
periodic wave:

7. IN PHASE / OUT OF PHASE
• In phase
• when 2 points on a wave that are an integer (full number)
multiple of wavelength apart from each other and have a phase
difference of 2pi
• points have equal displacements at ALL TIMES
• Out of phase
• 2 phase that are an odd half-integer multiple (1/2, 3/2, 5/2…) of a
wavelength apart are pi rad out of phase with each other
• points ALWAYS have equal and opposite displacements from
equilibrium