If the output of this figure below has been minimized. What might happen to this minimum if the frequency of the AUDIO OSCILLATOR was changed (say by 10%)?
Can I suggest that the output of the adder is better described by the expression:
y(t) = V1Sin(2.Pi.f1.t) + V2.Sin(2.Pi.f1.t + Phi)
The frequency of both signals into the adder will be the same, the phase shifter will not (should not) change the frequency, all that should happen it that there is a phase shift (Phi).
Is this a homework question? Think about what minimising the sum implies. How much phase shift is needed to give the minimum (assuming g and G are constant)?
I agree that the phase shifter should not alter the frequency because just shifting phase does not alter the frequency. So the equation for the sum will have both frequencies the same f2=f1.
To know the amplitude we'd have to know how much the phase shifter altered the amplitude. Phase shift circuit almost always alter the amplitude, so that's important to know. But if it does not alter the amplitude, then V2=V1 also.