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# A signal of 5kHz frequency is amplitude modulated on a carrier wave of frequency 2 MHz. The frequencies of the resultant signal is/areA) 2 MHz onlyB) 2005 kHz and 1995 kHzC) 2005 kHz, 2000 kHz, and 1995 kHzD) 2000 kHz and 1995 kHz

Last updated date: 12th Sep 2024
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Hint: In amplitude modulation, the amplitude (signal strength) of the carrier wave is in proportion to that of the input signal, such as an audio or video signal. Amplitude modulation is done to transmit low-frequency signals over large distances without power losses.

Modulation is a process of combining a signal with a sinusoid to produce a new signal with different properties. This new signal, conceivably, will have certain benefits over an un-modulated signal due to its different properties. Mixing of low-frequency signals with high-frequency carrier signals is called modulation.
Amplitude modulation (AM) is a modulation technique used in electronic communication, most commonly for transmitting messages with a radio carrier wave.
The bandwidth of the resultant signal is twice the bandwidth of the modulating signal since the upper and lower sidebands around the carrier or the input signal frequency each have a bandwidth as wide as the modulating frequency. So, in our case, the modulating frequency is${f_C} = 2{\text{ }}MHz = 2000\,kHz$.
Hence the frequency of the resultant signal will have frequencies of
${f_R} = {f_C} + {f_m} = 2000\,kHz + 5\,kHz = 2005\,kHz$
${f_R} = {f_C} - {f_m} = 2000\,kHz - 5\,kHz = 1995\,kHz$

So, the frequency content of the resultant wave will have frequencies 1995kHz, 2000kHz and 2005kHz

Note: The way amplitude modulation such that bandwidths of frequencies are emitted from the resultant signal will have a bandwidth of frequencies depending on the way the modulation is carried out. In our case, the modulated frequencies can have values between the resultant frequencies as well as the modulation frequency itself. Modulation is required since low-frequency signals which contain the data cannot be emitted over the atmosphere since they will be scattered immensely while a higher frequency wave will not be scattered as much. There are different kinds of modulation possible to solve this issue: amplitude modulation, frequency modulation, and phase modulation.