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The modulation frequency of an AM radio station is 250 Hz, which is $10%$of the carrier wave. If another AM station approaches you for license what broadcast frequency will you allot?
(A) 2750 Hz
(B) 2000 Hz
(C) 2250 Hz
(D) 2900 Hz

Last updated date: 15th Jun 2024
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Hint: We know that frequency modulation (FM) is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave. The term and technology are used in computing, signal processing and telecommunications. Usually, a high-frequency sine wave is used as a carrier wave signal. These modulation techniques are classified into two major types: analog and digital or pulse modulation. When the audio signal is modulated onto the radio frequency carrier, the new radio frequency signal moves up and down in frequency. The amount by which the signal moves up and down is important. It is known as the deviation and is normally quoted as the number of kilohertz deviations.

Complete step by step answer
Let us first know the need of modulation. Modulation allows us to send a signal over a bandpass frequency range. If every signal gets its own frequency range, then we can transmit multiple signals simultaneously over a single channel, all using different frequency ranges. Another reason to modulate a signal is to allow the use of a smaller antenna.
It is known that radio waves are electromagnetic waves with the longest wavelengths, lowest frequencies, and least amount of energy. They are used for radio and television broadcasts and many other purposes. In radio broadcasts, sounds are encoded in radio waves by changing either the amplitude (AM) or frequency (FM) of the waves.
We know that AM wave frequency contains 3 frequencies, which are given as:
$f_{c}, f_{c}+f_{m}, f_{c}-f_{m}$
Now we can say that here,
$f_{c}=\dfrac{250}{0.1}=2500 k H z$
$f_{m}=250 k H z$
Hence, the range of signal of the given radio station is $2250 \mathrm{kHz}$ to $2750 \mathrm{kHz}$.
So, we will allot another AM station broadcast frequency which will not overlap with this range.
So only the option $2000 \mathrm{kHz}$ can be chosen as broadcast frequency for another AM station as range for that will be $1800-2200 \mathrm{kHz}$.
Therefore, we will allot $2000 \mathrm{kHz}$ broadcast frequency to another AM station.

Hence, the correct option is B.

Note: It is known that waves can be modulated, either in amplitude, frequency, or phase, to carry or transmit images, music, speech, or other signals. A carrier system is a telecommunications system that transmits information, such as the voice signals of a telephone call and the video signals of television, by modulation of one or multiple carrier signals above the principal voice frequency or data rate. For the transmission of audio signals at distant places, the high frequency carrier waves are used, because these frequency carrier waves travel through space or medium with the speed of light and they are not obstructed by earth's atmosphere.

We should have an idea that FM systems have a much wider bandwidth than AM systems and therefore more prone to selective fading. FM transmitters and receivers require booster circuits as they have poorer signal to noise ratio at high audio frequencies.