Question #42869

Two harmonic signals of frequencies $f_1$ and $f_2$ ($f_1 > f_2$) are fed into a phase detector. At $t = 0$, the signals are perfectly in phase. The phase detector outputs a voltage $V(t) = \alpha \Delta \phi(t) + V_0$, where $\Delta \phi(t)$ is the instantaneous phase difference between the signals, $\alpha = \frac{5}{\pi} \text{ mV/rad}$ is the calibration constant, and $V_0 = 16 \text{ mV}$ is a systematic zero-error (DC offset). A student wishes to determine the beat frequency $f_b = f_1 - f_2$. They calculate the ideal target voltage $V_{ideal}$ that corresponds to exactly $N = 8$ beats, assuming no zero-error. The student then measures the time $T$ it takes for the actual output voltage $V(t)$ to reach this calculated $V_{ideal}$ from $t=0$. Using the measured time $T$, the student calculates the apparent beat frequency as $f_b^* = \frac{N}{T}$ and finds it to be $5.0 \text{ Hz}$. What is the true beat frequency $f_b$?