Jenny Lee, PHYS 101 LJ2

PHILIP (YOUR ULTIMATE

GUIDE ON WAVES)

…

BROOOO

• phase is NOT A FIXED QUANTITY!

• TEXTBOOK SAYS: “Phase is a variable that depends on position and time.”

𝜑 𝑥, 𝑡 = 𝑘𝑥 ± 𝜔𝑡 + 𝜑

𝜑 𝑥, 𝑡 =2𝜋

λ𝑥 ± 2𝜋𝑓𝑡 + 𝜑

• PHILLIP SAYS: We know that the equation for a sinusoidal wave is 𝐷 𝑥, 𝑡 = 𝐴𝑠𝑖𝑛(

2𝜋

λ𝑥 − 2𝜋𝑓𝑡 + 𝜑).

The 2𝜋

λ𝑥 component refers to position, and the

2𝜋𝑓𝑡 component refers to time. In the D(x,t) equation, 𝜑 refers to the phase constant, which you can think of as how much the sin/cos equation has shifted horizontally from a graph of sin(x) or cos(x), or the head start that a wave has.

Don’t you hate

complicated textbook

explanations? Well, with my

expertise as a surfer and

physicist I can help you.

Let’s talk about what phase

and phase difference is.

• In simple terms: phase is whatever is found inside the brackets of the sin

or cos equation.

• 𝑫 𝒙, 𝒕 = 𝑨𝒔𝒊𝒏 𝒑𝒉𝒂𝒔𝒆 𝒐𝒓 𝑨𝒄𝒐𝒔(𝒑𝒉𝒂𝒔𝒆)• It is important to remember that D(x,t) forms a 3D plot, and so it is

dependent on two variables.

• If we observe 2 waves at the exact same position over time, we can say

that their phases are 𝜑1 = 𝑘𝑥0 +𝜔𝑡1 + 𝜑 and 𝜑2 = 𝑘𝑥0 + 𝜔𝑡2 + 𝜑respectively. The phases indicate at what point of the sinusoidal cycle the function is currently at.

Pretty

sick,

huh?

• PHILIP SAYS: The phase difference, ∆𝜑, can be thought of as the value between two different phases.

∆𝜑 = 𝜑2 − 𝜑1

• If we plug in the two phases we identified earlier, we can determine the phase constant.

∆𝜑 = (𝑘𝑥0 +𝜔𝑡2 + 𝜑)− (𝑘𝑥0 + 𝜔𝑡1 + 𝜑)= 𝜔𝑡2 + 𝜑 − 𝜔𝑡1 +𝜑

This represents an instance where two sinusoidal waves with different initial displacements are observed at one position over time, and we

would like to know what the difference between their phases are.

• After every race, Phillip graphs out the wave that he has

ridden on. Sometimes, these waves are in-phase:

(This is known as constructive interference)

Other instances, the waves are out of phase.

(This is known as destructive interference)

As a professional

surfer, I like to

know the

characteristics of

a wave I’ve

been racing on.

𝜑2 − 𝜑1 = 𝑛 λ

The phase difference of

such waves are an even

multiple of pi.

𝜑2 − 𝜑1 = (𝑛 + 0.5) λ

The phase difference of

such waves are an odd

multiple of pi.

(Phillip hopes that you will never confuse phase,

phase difference, and phase constant again.)