PHASE AND PHASE DIFFERENCE

Learning Objects 3 Physics 101

A BIT OF REVIEW:

You may remember learning about standing waves in the past. These waves oscillate and create regions where the disturbance of the wave is almost zero. These ‘nodes’ create the illusion that the wave is standing still.

A BIT OF REVIEW

In comparison, travelling waves do not have nodes and hence the wave is seen to ‘travel’ and alter its displacement from its equilibrium position as time progresses

EQUATIONS

The (x) in the usual displacement equation: D(x) = Asin(kx) Is now replaced with: (x-vt) for waves traveling in the positive x direction (x+vt) for waves traveling in the negative x direction

Compared to the previous equation, the new variables allow room for us to shift the graph by shifting it by a phase difference

PHASE

The phase of a wave is dependant on position and time and allow us flexibility to describe the graph with a variety of different notations

PHASE DIFFERENCE

Here, we can take the cosine wave to be our reference. The sine waves can be described as being ahead of the cosine wave by π/2 . This means that there is a phase difference of π/2 between the two waves. The phase difference is the difference between the phases at two points at the same time t. Oscillations can have phase differences of any multiple of π. However, if they have a phase difference of either 0 or 2π they are said to be in phase.

QUESTION

A harmonic wave A has a phase difference of 3π/2 ahead of harmonic wave B. Part I: Sketch and label the two waves. Part II: Show the relationship between the

phase difference in the question above and the distance between points (x) in multitudes of wavelength (λ)

SOLUTION PART II

These points are “off” or out of phase by 3π/2. As noted, the blue wave will be labeled as A and the red wave will be labeled as B

As shown here, the crests on the two waves still differ by 3π/2.

3π/2

SOLUTION PART II

= 2π (∆ x/λ) We know that the phase difference ∆Φ

is given to us in the equation as 3π/2 Plugging this number into the equation

and solving for ∆x yields: ∆x =3π/2 = 2π (∆ x/λ)

Giving us the answer: ∆x=3 λ /4