GATE EC 2025 Set 1 Q4 — Analog Communications

Consider a frequency-modulated (FM) signal

$$f(t)=A_{c} \cos \left(2 \pi f_{c} t+3 \sin \left(2 \pi f_{1} t\right)+4 \sin \left(6 \pi f_{1} t\right)\right)$$

where $A_{c}$ and $f_{c}$ are, respectively, the amplitude and frequency (in $\mathrm{Hz}$ ) of the carrier waveform. The frequency $f_{1}$ is in $\mathrm{Hz}$ , and assume that $f_{c}>100 f_{1}$.

The peak frequency deviation of the FM signal in $\mathrm{Hz}$ is $\_\_\_\_\_\_\_\_$.