# Phase difference of reflected waves

The Phase difference of 2 travelling waves is how much one wave has shifted from the other, 'angle wise'

It's constant if both waves travel at the same speed. https://www.desmos.com/calculator/lrekw2jxpd

I learnt that the phase difference of a reflected wave is $$\pi$$, but what does 'phase difference' even mean here. The waves are travelling in opposite directions and hence there's no 'phase difference' (or at least a constant one) https://www.desmos.com/calculator/umtrrvxlkn .
If you reflect a wave, you can always tell a time, t for which the phase difference between the original and reflected wave is $$0, \pi, 2\pi..$$(any real number). So what do people mean when they say that the phase difference is $$\pi$$?

It means that when primary wave is expressed as $$y_p(x) = A_p\cos (\Omega t - kz),~~~A_p > 0$$ so it moves in direction of $$z$$-axis, and reflecting wall is at $$z=0$$, then reflected wave is expressed as $$y_r(x) = A_r\cos (\Omega t + kz +\pi),~~~A_r > 0$$ which means that at $$z=0$$, the reflected wave value $$y_r(0)$$ has opposite sign to incoming wave $$y_p(0)$$.
So the phase shift $$\pi$$ refers to values of both waves on the boundary.
This shift $$\pi$$ happens only for the reflected wave that is reflected back to medium with lower phase speed. For example, when light travelling in air is reflecting from the air-glass boundary back to air.
• Yes the phase difference concers only the point where the reflection happens. The phase is off by $\pi$ only some reflections, see above. Feb 7, 2021 at 16:23