 # Mam, what is the difference between phase difference and path difference

Mam, what is the difference between phase difference and path difference.can you also explain me with a example?

Path difference and phase difference is for the waves of same frequency and it is used to determine constructive and destructive interference in waves. Path difference (measured in terms of wavelength) : It is the actual measurable difference between lengths of path travelled by two waves. It is represented as ? x or ?.

In the above diagram, the path difference between the red and blue wave is (lambda)? / 4.

Phase difference (measured in radians) : It is the difference in phase of two waves of same frequency. It is represented by ??.

In the above diagram, the blue wave leads the red wave by a phase difference of pi/2.
At time t = 0, the blue wave has displacement equal to 0, while that of red wave has negative displacement (-A).

At pi/2, the blue wave has maximum positive displacement(+A), while that of red wave is zero.
Hence Blue wave is leading by a phase difference of pi/2 and path difference of (lambda) ? /4.

Example:
Suppose two horses are running in a circular track with same speed and in same direction but their starting point is different. They will cross the same point at different times but there will be constant difference in time, each time they cross the point. Thus we can say that they are moving with constant phase difference. This is analogous to the two waves travelling with same frequency with some phase difference i.e. their starting point is different.

Relation between path difference and phase difference is given by, phase difference (??) = (2/?)* path difference (?x)