A sinusoidal message $()=2$ sin $()$ is FM modulated on a carrier $()=102$ cos $().$ The frequency

deviation constant of the modulator is $=2103$ rad$/$s$/$V$.$ The message frequency is $12$ kHz and the carrier

frequency is $300$ kHz$.$ Determine, with appropriate units,

a$)$ The instantaneous frequency $()$ and the peak frequency deviation of the FM signal.

b$)$ The peak phase deviation.

c$)$ Modulation index.

d$)$ The approximate bandwidth of the FM signal $($Hint: Use Carson$$s rule$).$