How to Explain Wave Phase Difference Physically?

[mcquarr]

I am asked to define the phase of a complex function (a wave) in words and physically. I don't know a better way than to draw two different sine functions and show the phase difference on the graph...Any suggestions?

 

[Mentz114]

Not much more to it. You could write a wave equation -

$$\phi = e^{i(kx - \omega t)}$$

and transform with a phase change

$$\phi ' = e^{i(kx - \omega t + \theta)}$$

 

[Demystifier]

I am asked to define the phase of a complex function (a wave) in words and physically.

What kind of wave? A quantum wave function? A classical wave?