Phase constant and reflection of waves

1. The problem statement, all variables and given/known data
If two waves are created at x = 0 and t = 0 (and are in phase to begin with), and are then sent traveling along a string in the positive x direction, and they get reflected at the end of the string, there will be a similar pair of waves traveling in the negative x-direction. The two waves have a differing frequency.
Now my question is whether there a phase angle associated with these wave (namely the reflected waves).
Like for the waves traveling in the positive direction:
[itex]ψ_{1}(x, t)[/itex] = Asin(([itex]ω_{1}/v[/itex])x – ([itex]ω_{1}[/itex])t + θ)
[itex]ψ_{2}(x, t)[/itex] = Asin(([itex]ω_{2}/v[/itex])x – ([itex]ω_{2}[/itex])t + θ), would θ = 0 (the phase constant) in both these cases ?

And the reflected waves:
[itex]ψ_{1}(x, t)[/itex] = Asin(([itex]ω_{1}/v[/itex])x + ([itex]ω_{1}[/itex])t + θ)
[itex]ψ_{2}(x, t)[/itex] = Asin(([itex]ω_{2}/v[/itex])x + ([itex]ω_{2}[/itex])t + θ), would θ = 0 in these cases as well?
I’m really confused about this??

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