Question

A signal of $5kHz$ frequency is amplitude modulated in a carrier wave frequency $2MHz$. What are the frequencies of the side bands produced?

Answer 1

Hint: Frequency of carrier wave and amplitude modulated wave is given and to find the side band frequencies you need to take addition of those two frequencies and difference of those two frequencies and these results will be the side band frequencies.

Complete answer:
Carrier wave: It is a waveform (usually sinusoidal) that is modulated (modified) with an information bearing signal for the purpose of conveying information. This carrier wave usually has a much higher frequency than the input signal does. The purpose of the carrier is usually either to transmit the information through space as an electromagnetic wave (as in radio communication), or to allow several carriers at different frequencies to share a common physical transmission medium by frequency division multiplexing (as in a cable television system).
Here carrier wave frequency
${f_m} = 2MHz = 2000KHz$
And modulated wave frequency is
${f_c} = 5Khz$
Now upper band frequency is
${f_m} + {f_c} = 2000 + 5 = 2005KHz$
And lower band frequency is
${f_m} - {f_c} = 2000 - 5 = 1995KHz$
Therefore, side band frequencies are: $2005KHz\& 1995KHz$

Hence final answer is $2005KHz\& 1995KHz$.

Note: A carrier wave is a pure wave of constant frequency, a bit like a sine wave. By itself it doesn’t carry much information that we can relate to (such as speech or data). To include speech information or data information, another wave needs to be imposed, called an input signal, on top of the carrier wave. This process of imposing an input signal onto a carrier wave is called modulation. In other words, modulation changes the shape of a carrier wave to somehow encode the speech or data information that we were interested in carrying. Modulation is like hiding a code inside the carrier wave.