A (sinusoidal) carrier wave is amplitude modulated by a (sinusoidal) message signal

Question

A (sinusoidal) carrier wave 

C(t) = A_c sin ω_ct

is amplitude modulated by a (sinusoidal) message signal

_{m(t) =} A_m sin ω_m t

Write the equation of the (amplitude) modulated signal. Use this equation to obtain the values of the frequencies of all the sinusoidal waves present in the modulated signal.

Answer 1

The equation of the (amplitude) modulated signal is

C_m (t) = [(A_c + A_m sin ω_c t

This can be rewritten as

C_{m(t) = (A (1 +} μ sin  ω_m t)] sin ω_ct 

Where μ = A_m / A_c = modulation index

These are the three sinusoidal wayes present in the amplitude modulated signal.

The frequencies of these three waves are