Is the biggest phase difference pi?

[MBBphys]

Homework Statement

So, my teacher said that the biggest phase difference is pi. But what if you have two waves arriving at a point, such that the instruction from one wave is a phase of (7pi/4), and from the other is (3pi/4), then the phase difference is (9pi/8), which is larger than pi. So, was she right or wrong? Or have I made a mistake?
Thanks!

Homework Equations

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The Attempt at a Solution

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[azizlwl]

Imaging you and your friend running in a race around a circular track, what is biggest separation between two of you in radian

 

[Dr. Courtney]

It depends on if you are only looking at a limited span of time or if you can go all the way back to the beginning of the signals.

The biggest phase difference one can detect in a time window when both signals are present is pi. If you can go all the ay back to the beginning, you can detect much larger phase differences.

 

[MBBphys]

Imaging you and your friend running in a race around a circular track, what is biggest separation between two of you in radian

What you say makes complete sense: the biggest difference we can be is such that the line between us would be the diameter of the circle and the angle is 180 degrees or pi radians. But how does that translate to a wave though? Why is the example of a bigger than pi phase I gave wrong?
Thanks!