Question

The number of amplitude modulated broadcast stations that can be accommodated in a $300kHz$ bandwidth for the highest modulating frequency 15kHz will be:
A. 20
B. 10
C. 8
D. 15

Answer 1

In this problem, we are given the bandwidth and the highest modulated frequency. Therefore, we need to use the relation among bandwidth, highest modulating frequency and number of amplitude modulated broadcast stations to find the correct answer.

Formula used:
$B.W. = 2 \times n \times H.M.F.$, where, $B.W.$ is the bandwidth, $n$ is the number of amplitude modulated broadcast stations and $H.M.F.$ is the highest modulating frequency

Complete step by step solution:
First of all, let us see why modulation is required. An electronic signal cannot be transmitted in the audio frequency (AF) range (baseband signal frequency less than $20kHz$) over a long distance directly due to the three main reasons: Size of the antenna or aerial, Effective power radiated by an antenna and Mixing up of signals from different transmitters. The process of modulation is required to overcome these issues. There are three types of modulation: Amplitude modulation (AM), Frequency modulation (FM) and Phase modulation (PM).Here, we are given the case of amplitude modulation. We know that,
$B.W = 2 \times n \times H.M.F.\\\ \Rightarrow n = \dfrac{{300}}{{2 \times 15}} = 10$
In the question, it is given that bandwidth is $300kHz$ and for the highest modulating frequency is $15kHz$.
$\therefore n = \dfrac{{300}}{{2 \times 15}} = 10$
Thus, 10 amplitude modulated broadcast stations can be accommodated in a $300kHz$ bandwidth for the highest modulating frequency $15kHz$.

Hence, option B is the right answer.

Note: The type of modulation is based on the varying parameter. If the amplitude of the high frequency carrier wave is varied with the instantaneous amplitude of the modeling signal, it is known as amplitude modulation, if the frequency of the carrier wave is varied with the instantaneous amplitude of the modeling signal, it is known as amplitude modulation and if the phase of the high frequency carrier wave is varied with the instantaneous amplitude of the modeling signal, it is known as amplitude modulation.