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

Bandwidth is nothing but the maximum rate of data transfer within a given path. Generally for waves modulation is done to increase their potential of carrying information through long distances. Modulated waves are sent from transmission stations while they are demodulated at receiving stations.

Formula used:
$n = \dfrac{{B.W}}{{2f}}$

Complete step by step answer:
Modulation can be explained by the general example. Let us consider the simple instance which we use in our daily life. If one wants to throw a piece of paper through a very long distance it's not possible if we just throw that paper, we fold that paper to some weight, let it be a stone and throw that paper folded stone. Then that paper can reach very longer distances. Similarly in communication systems modulation plays a key role. Here the message signal which we like to transmit is analogous to paper and the carrier signal is analogous to stone and the person who throws paper is analogous to the transmitter.
Three important factors that justify the need of modulation are

1. Actual antenna/aerial size

2. Effective power which is radiated by antenna

3. Signals from different transmitters getting mixed up

4. Actual antenna size: In case of transmission systems antenna size matters. Generally bigger size antennas have big range but bigger antennas might not be always optimal while it depends on transmission frequencies too. Low frequency signal requires bigger antennas but after modulation frequency of message signal gets increased which allows us to use smaller antennas

5. Effective power which is radiated by antenna: when frequency is increased its wavelength decreases which inturn increases the radiated power

6. Signals from different transmitters getting mixed up: signals getting mixed up causes signal interference which causes deviation In original waveform. The process of nullification of this interference is done by modulation.
   Number of stations(n) that can be accommodated in a given bandwidth (B.W) for the highest modulating frequency(f) will be
   $n = \dfrac{{B.W}}{{2f}}$
   Band width is given as 300 kilohertz and maximum frequency is given is 15 kilohertz. So the number of stations will be
   $n = \dfrac{{B.W}}{{2f}}$
   \eqalign{ & \Rightarrow n = \dfrac{{300kHz}}{{2 \times 15kHz}} \cr & \Rightarrow n = \dfrac{{300kHz}}{{30kHz}} \cr & \therefore n = 10 \cr}

Hence option B will be the answer.

Note:
Usually due to the amplitude modulation electromagnetic noise will be generated and this is the one of the disadvantages of the modulation. The frequency of the signal transmitted will decide the size of the antenna. Modulation and demodulation are usually done by the devices called modems.