The amplitude modulated signal consists of two sinusoidal waves of frequencies, (`omega_c→`angular frequency of carrier wave) (`omega_m→`angular frequency of modulating signal)

Options

A. `omega_c/2,omega_m/2`
B. `(omega_c+omega_m)/2,(omega_c-omega_m)/2`
C. `omega_c/omega_m,omega_c^2/omega_m^2`
D. `omega_c+omega_m,omega_c-omega_m`

Answer

To solve the problem regarding the amplitude modulated (AM) signal consisting of two sinusoidal waves of frequencies, we can follow these steps:

### Step 1: Understand the Concept of Amplitude Modulation
Amplitude modulation involves varying the amplitude of a carrier wave in accordance with the amplitude of a modulating signal. The carrier wave has a frequency denoted by \( \omega_c \) (angular frequency), and the modulating signal has a frequency denoted by \( \omega_m \).

**Hint:** Remember that in amplitude modulation, the carrier wave is modified by the modulating signal.

### Step 2: Identify the Frequencies in AM
In amplitude modulation, the output signal will contain the carrier frequency and two side frequencies. The side frequencies are generated by adding and subtracting the modulating frequency from the carrier frequency. Thus, the frequencies present in the modulated signal are:
- Carrier frequency: \( \omega_c \)
- Lower side frequency: \( \omega_c - \omega_m \)
- Upper side frequency: \( \omega_c + \omega_m \)

**Hint:** The side frequencies are derived from the carrier frequency by adding and subtracting the modulating frequency.

### Step 3: Write Down the Frequencies
From the above understanding, we can summarize the frequencies present in the amplitude modulated signal:
1. \( \omega_c - \omega_m \) (lower side frequency)
2. \( \omega_c \) (carrier frequency)
3. \( \omega_c + \omega_m \) (upper side frequency)

**Hint:** Make sure to list all frequencies that result from the modulation process.

### Step 4: Conclusion
The amplitude modulated signal consists of three frequencies: \( \omega_c - \omega_m \), \( \omega_c \), and \( \omega_c + \omega_m \). However, the question specifically asks for the two sinusoidal waves of frequencies that are most relevant, which are the side frequencies: \( \omega_c - \omega_m \) and \( \omega_c + \omega_m \).

**Hint:** Focus on the side frequencies when asked about the frequencies of the modulated signal.

### Final Answer
The amplitude modulated signal consists of two sinusoidal waves of frequencies: \( \omega_c - \omega_m \) and \( \omega_c + \omega_m \).