Write any two factors which justify the need for modulating a signal. Draw a diagram showing an amplitude modulated wave by superimposing a modulating signal over a sinusoidal carrier wave.

Hint: In order to solve this question you have to know about the modulation, how many types of modulation are there? What is the amplitude modulation? How can we implement it? Recall all the factors which we need to modulate our signal. Then draw a properly labeled diagram.

Complete step by step solution:
Two factors that justify the need for modulating a signal are:
1) Height of antenna:
Let us assume a signal of $10kHz$ is to be transmitted, then the wavelength of the transmitted signal is given by,
$\lambda = \dfrac{c}{\nu }$ where, $c$ is the speed of the light and $\nu $ is the frequency of the transmitted signal.
$ \Rightarrow \lambda = \dfrac{{3 \times {{10}^8}}}{{10 \times {{10}^3}}} = 30km$
The height of the transmitting antenna must be of the order of wavelength λ of the transmitted signal.
So, the maximum antenna height is $h = \dfrac{\lambda }{4}$
$ \Rightarrow h = \dfrac{{30}}{4} = 7.5km$
It is impossible to erect such a tall antenna. Therefore, we have to modulate the signal in order to increase the frequency, as the frequency increases, the wavelength decreases and hence the maximum antenna height decreases.

2) Effective Power radiated by an antenna:
Power radiated by a linear antenna is given by,
$P \propto \dfrac{1}{{{\lambda ^2}}}$
As after modulation the frequency of the signal is increased that results in the decrease in the wavelength and then according to the above formula power radiated is increases as the wavelength decreases.
Therefore, in order to increase the power radiated we have to modulate the signal.




Note:
There are three basic types of modulation:
Amplitude modulation: It is a type of modulation in which the amplitude of the carrier signal is changed with respect to the modulating signal. The frequency and phase remain constant in amplitude modulation.
Frequency modulation: It is a type of modulation in which the frequency of the carrier signal is changed with respect to the modulating signal. The amplitude and phase remain constant in this frequency modulation.
Phase modulation: It is a type of modulation in which the phase of the carrier signal is changed with respect to the modulating signal.