Final answer:
The frequency deviation constant is equal to the peak-frequency deviation divided by the peak amplitude of the modulating signal.
Step-by-step explanation:
Frequency modulation (FM) is a method of encoding information onto a carrier wave by varying its frequency. In this case, the carrier wave is represented by c(t) = 10 cos(2πft), where f is the frequency of the carrier wave, which is 10^6 Hz. The signal m(t) = 3 cos(2000πt) is modulating the carrier wave.
The peak-frequency deviation is the maximum change in frequency due to modulation. In this case, the peak-frequency deviation is 5 kHz.
The frequency deviation constant, represented by Δf/Δm, is equal to the peak-frequency deviation divided by the peak amplitude of the modulating signal. In this case, the peak amplitude of the modulating signal is 3.
Therefore, the frequency deviation constant is 5 kHz / 3.