Phase difference and path difference

[Misr]

Hello,
What are phase difference and path difference?
Can you give me a simple explanation so that I could imagine
It would be great if there are some illustrations
Thanks

 

[grzz]

Consider two particles performing simple harmonic motion. Like two masses hanging on two different vertical springs. If the masses go to the maximum height together and go to the lowest height together, then the two particles move in phase with each other. But if when one is at the bottom, the other is at the top, then they are out of phase with each other by half a period (or by 180 degress or by pi radians).

 

[grzz]

The diagram can represent a wave going along a rope.
The two arrows at the crests are in the same direction - showing that those two parts of the rope are moving in phase with each other. The path difference between these two (consecutive) crests is one wavelength, i.e.the distance the wave travels in one period.

 

[Misr]

The path difference between these two (consecutive) crests is one wavelength

how?

 

[grzz]

Two points on a wave, one on a crest and the other one on a trough (which immediately follows the crest), can be distinguished by:
a) phase differece i.e. 180 degrees or pi radians;
b) time difference i.e. half a period;
c) distance difference i.e. half-wavelength.

Note that the distance between two consecutive crests is called 'wavelength'.
e.g. the frequency of a wave is the number of wavelengths going through in 1 second.

 

[Born2bwire]

The diagram can represent a wave going along a rope.
The two arrows at the crests are in the same direction - showing that those two parts of the rope are moving in phase with each other. The path difference between these two (consecutive) crests is one wavelength, i.e.the distance the wave travels in one period.

Typically when we are talking about path difference when it comes to traveling waves is that we are discussing literally the difference in the distance traveled by two different waves. Take for example if we have a source in a room where a receiver is also placed. There are multiple paths that the waves from the source can take to reach the receiver. The primary path is the direct path between the source and receiver. But there is also a possible path due to reflections from the walls of the room. You have a path where you have a single reflection, two reflections, etc. Each of these will reach the receiver but they will have relative path differences due to the different total distances travelled.

The relative path difference is important because the phase of a wave progresses as it travels over a distance. So because these waves have a relative path difference, they will also have a relative phase difference which can give rise to interference. This occurs despite the fact that when they were originally produced at the source they did not have a phase difference.

So the path difference can be taken to be the difference between the distance traveled by two different waves or it can also be taken as the phase difference that arises between two waves due to the different distances travelled.

EDIT: The double slit interference is a good visual example of interference due to the path difference. The two slits produce waves that start out with no relative phase difference. But the interference arises because the two waves usually have to travel different distances to reach a certain point.