what does it mean by path difference and phase difference plz explain me in detail
Path difference and phase difference is meaningful for waves of same frequency and it is used to determine constructuve and destructive interference in waves.
Path difference (measured in terms of wavelength) is the actual measurable difference in distance that two waves travel from a source to a common point. In my diagram the path difference between the red and blue wave is lambda / 4 . (For this measure the distance between any two consecutive crests or trough in terms of wavelength)
Phase difference (measured in radians) is the difference in the phases of the two sinusoidal waves of same frequency. In my diagram the blue wave leads the red wave by a phase difference of pi/2 (or 90 degrees). It is denoted in the equation of the wave in the argument of sine.
(Wt - pi/2) is the phase at any time, while -pi/2 is the phase difference.
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
There is a relation between path difference and phase difference. You know that one oscillation is completed in 2pi radian which is equivalent to wavelength (lambda)
So path difference of one wavelength is equal to phase difference of 2pi radian.
Path difference of one unit is equal to phase difference of 2*pi / lambda
And path difference of x is equal to phase difference of (2*pi / lambda) x = kx
The term [k = 2*pi / lambda] is a constant called wave number.
For constructive interference, the waves should differ by a path difference of integral multiple of wavelength, lambda, 2 lambda, 3 lambda, so on.
This is equal to phase difference of 0, 2pi, 4pi, 6pi.... .....even multiple of pi.
For destructive interference, the path difference should be odd integral multiple of half-lambda
( lambda /2,
3 lambda /2,
5 lambda / 2
This is equal to phase difference of (pi, 3pi, 5pi, 7pi, odd multiple of pi.