Two-Port Model: "What is the amplitude of the input signal?" Solution Misunderstanding
There's a difference between the amplitude of a signal and the RMS wich is used for power calculations. The amplitude is \$\hat{V}\$.

$$P = \frac{V_{eff}^2}{R}$$


  $$V_{eff} = \frac{\hat{V}}{\sqrt{2}} \rightarrow V_{eff}^2 = \frac{\hat{V}^2}{2}$$


This is where the 2 is coming from.