Difference between phase difference and path difference

In summary, Path difference is the difference (in meters) between the lengths of two paths. Phase difference is the difference (in degrees) between the phases of two waves.
  • #1
logearav
338
0
respected members,
could anyone explain the difference between path difference and phase difference ? what does the term phase exactly mean? thanks in advance
 
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  • #2
Path difference is the difference (in meters) between the lengths of two paths.

In periodic phenomena, the phase is the relative position in the cycle. That is if you divide all the cycle in 360 degrees (or better in 2 pi radians), and decide to start counting at a given position. Each time that the process attains the same position its phase will have advanced 360 degrees.
Take as periodic process a walking person, and place the start of phase when the right foot touches the earth. When the phase advances 180°, the left foot touches the earth. See why?
No take two persons walking beside. They start touching the Earth with their right foot simultaneously: they are in phase, their phase difference is zero.
If they are parading soldiers they will stay in phase and their right foots will continue to touch the Earth simultaneously.
But if they are not parading, the pace period of each one will be probably different. If the period of person B is shorter, his right foot will touch Earth a little before person A. We say that person B is in advance on phase relative to A. Or that phase of A lags B. If the periods of each one stay so, the difference of phase will increase. Eventually B will be 180° in advance (or B 180° in retard).

When two waves have the same periodicity, that is same frequency, and travel at the same speed, if they travel the same distance they will keep the same phase difference. But if one of the waves has to travel a longer path it will be in retard of phase.
 
  • #3
Consider a lightsource that emits a monochromatic wave A(x,t),

Code:
                      _         _
	            /   \     /   \
      	           /     \   /     \
                 x/       \_/       \_...       Wave A(x,t)

<-----d--------->
     _        _         _
   /   \     /  \     /   \
  /     \   /    \   /     \
x/       \_/      \_/       \...       Wave B(x,t)

and another lightsource emitting a wave B(x,t) below the first one that is shifted to the left by
the distance d. Both waves shall have the same frequency. This distance d is called path difference.
We say: These two waves have the path difference d.

What is the phase difference?
To answer this question we first have to look at the definition
of the phase. The phase occurs with the mathematical form of a wave:

[tex]A(x,t) = A_{0} \cdot sin(kx-\omega t)[/tex]

Definition: The phase is the term in the brackets of the sin-function, so

[tex]\mbox{phase}=kx-\omega t[/tex]

The phase is often denoted by the greek letter [tex]\phi[/tex],
so let us also write:

[tex]\phi = kx- \omega t[/tex]

Thus, our wave can be written as:

[tex]A(x,t) = A_{0} \cdot sin(\phi) = A_{0} \cdot sin(kx-\omega t)[/tex]

Now have a look at the second wave B(x,t). It is shifted to the left.
What does this shift mean?
Imagine that both waves travel to the right.
If you compare how far both waves travel, then you will notice
that the left-shifted wave travels farther by the path d.
This can be expressed mathematically:

[tex]B(x,t) = B_{0} \cdot sin(\phi_2) = B_{0} \cdot sin(k(x+d)-\omega t) = B_{0} \cdot sin(kx- \omega t +kd)[/tex]

What is the phase difference? It's the difference between [tex]\phi_2[/tex] and [tex]\phi[/tex],
thus:

[tex]\mbox{phase difference} = \mbox{Phase of wave } B(x,t) - \mbox{Phase of wave } A(x,t)}[/tex]
[tex]= \phi_2-\phi = (k(x+d)-\omega t)-(kx-\omega t) = kx+kd- \omega t-kx+ \omega t = kd[/tex]

Result: For a path difference d, we get a phase difference
[tex]\phi_2-\phi=kd[/tex]

We say The phase difference between the two waves is [itex]\phi_2-\phi=kd[/itex]

But remember: The general definition of the phase difference is

[tex]\phi_2 - \phi[/tex]

Questions for you:
(a) What happens with B(t) if [tex]kd = 2 \pi [/tex]? Call the result B_new(t) (Hint: sin(x+2Pi) = sin(x))
(b) What is the path difference between B_new(t) and A(t)?

(c) Let [tex]k= \frac{2 \pi}{500 \mbox{nm}}[/tex]. What is the phase difference between the two waves B(x,t) and A(x,t),
if I have a path difference of d=300 nm?
How do I have to choose the shift d such that the phase difference
is zero?
 
Last edited:
  • #4
thanks a lot, edgardo and lpfr for your informative clarifications. i ll solve the problem and get back to you.
 
  • #5
thanx first for this valuable explanation :)
Answers:
a) B_new(t) will be the same.
b)d= Q2-Q/K
c)Q3=6/5 pi
 
  • #6
Gr8 explanation from edgadro! Thanks!
 

What is the difference between phase difference and path difference?

Phase difference refers to the difference in the phase of two waves at a given point in time. It is measured in radians or degrees and can be positive, negative, or zero. Path difference, on the other hand, refers to the difference in the distance traveled by two waves from their source to a given point. It is measured in units of length, such as meters or centimeters.

How are phase difference and path difference related to each other?

Phase difference and path difference are related through the wavelength of the waves. The path difference between two waves that are in phase with each other is equal to an integer multiple of their wavelength. This means that the path difference is directly proportional to the phase difference.

What is the significance of phase difference and path difference?

Phase difference and path difference are important concepts in the study of waves and their behavior. They can help us understand interference patterns, diffraction, and other phenomena that occur when waves interact with each other.

What is the formula for calculating phase difference?

The formula for calculating phase difference is: phase difference = (path difference / wavelength) * 2π. This formula is based on the fact that the path difference is directly proportional to the phase difference and the wavelength is the distance traveled by a wave in one complete cycle.

How do phase difference and path difference affect the interference of waves?

Phase difference and path difference play a crucial role in the interference of waves. When two waves with a path difference that is equal to an integer multiple of their wavelength are in phase, constructive interference occurs, resulting in a larger amplitude. On the other hand, when the path difference is equal to half of the wavelength, destructive interference occurs, resulting in a cancellation of the waves' amplitudes.

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