For an amplitude modulated signal ω_m, and ω_c, are angular frequency of message signal and carrier wave respectively then AM signals contains frequencies 

Concept:

Amplitude modulation:

• It is the process in which the amplitude of the high-frequency carrier wave changes in accordance with the instantaneous value of modulating signals.
• During the positive half of the modulating signals, the amplitude of the carrier wave increases, similarly during the negative half of the modulating signals, the amplitude of the carrier wave decreases.
• The amplitude of the carrier wave changes according to the modulating signals.
• The amplitude of the carrier wave changes at the frequency ‘fm’ of the modulating signal.
• The frequency of the A.M. wave is equal to the unmodulated carrier frequency ‘fc’.

Explanation:

• The general expression of an amplitude-modulated wave for a single-tone message signal is given as:

⇒ sAM(T) = [Ac + Amcosωmt] cosωct

Where ωm = Frequency of the message signal, ωc = Carrier signal frequency

• The expression can be written as:

⇒ sAM(T) = Ac cosωct + Amcosωmtcosωct

We observe that the amplitude modulated signal has both the carrier frequency and the shifted frequency as shown:

• From the above diagram, it is clear that the amplitude modulated signal contains frequencies (ωc - ωm), ωc, and (ωc + ωm). Therefore option 4 is correct.

Important Points

• Bandwidth : The two sidebands lie on either side of the carrier frequency at equal frequency interval f. So, bandwidth = (fc + fm) - (fc - fm) = 2fm