# Intuitive explanation for why reflected waves change phase by $π$? [duplicate]

I have seen the equations that show the coefficient of reflection etc.

But I'm searching for an intuitive rather than solely mathematical explanation for why waves change phase by π when reflected (eg- from a solid wall)?

• Does this answer your question? Phase shift of 180 degrees of transversal wave on reflection from denser medium – FakeMod Apr 13 at 11:55
• After being reflected, the reflected wave combines with the incident wave to produce a standing wave pattern. If the medium is fixed at the boundary, there must be a standing wave node (zero amplitude) at the boundary. That requires that the displacement associated with the reflected wave at that point be equal and opposite to that of the incident wave. – R.W. Bird Apr 13 at 14:59

Key: stuff in double square braces is an identity used i.e.: $$\sin(x+\pi)=\sin(\pi-(-x))$$
$$[[\sin(\pi-z)=\sin(z)]]$$
$$\sin(x+\pi)=\sin(-x)$$ $$[[\sin(-x)=-\sin(x)]]$$ $$\sin(x+\pi)=-\sin(x)$$
• But switching direction of travel in general does not change the sign, eg. in general $f(x-ct)$ is not equal to $-f(x+ct)$ – user45664 Apr 13 at 17:19