Modulation index ,mf = \(\frac { Maximum\ frequency\ deviation }{ minimum\ signal\ freqency } \)

(i) Pulse Amplitude Modulation : Amplitude of the pulse varies in accordance with the modulating signal.

(ii) (ii) Pulse Position Modulation. : Pulse position (ie) time of rise or fall of the pulse ) changes with the modulating signal.

(i) In ground wave propagation, the conduction losses due to ground are very high at higher frequencies.
(ii) The space wave propagation has a limited line of sight distance due to curvature of earth.
(iii) At frequencies beyond 30 MHz, the sky waves pass through the ionosphere and are not reflected back. 

A transducer is a device which converts one form of energy into another.A microphone at the transmitting station and a loudspeaker at the receiving station are two examples of transducers. Infact a transducer provides output in electrical form or it has input in electrical form.

(i) Efficiency of AM transmission is low
(ii) Amplitude modulation suffers from noise
(iii) Quality of audio signal is often poor.

Here, A_m = 0.1 V, A_c = 0.2 V,\(\mu \)=?
\(\mu \)= \(\frac { { A }_{ m } }{ { A }_{ c } } =\frac { 0.1 }{ 0.2 } =0.5\)

Let N₁ and N₂ be maximum electron densities of the ionosphere on first and second days corresponding to 10 MHz and 8 MHz, respectively.
\(\therefore \left( \frac { { N }_{ 1 } }{ { N }_{ 2 } } \right) ^{ 1/2 }=\frac { { V }_{ c1 } }{ { V }_{ c2 } } =\frac { 10 \ MHz }{ 8 \ MHz }\)
\(\left( \frac { { N }_{ 1 } }{ { N }_{ 2 } } \right) ^{ 1/2 }=\frac { 5 }{ 4 } =\frac { { N }_{ 1 } }{ { N }_{ 2 } } =\frac { 25 }{ 16 } \)
\({ N }_{ 1 }:{ N }_{ 2 }=25:16\)

Microwaves are the electromagnetic waves of wavelength of the order of a few millimeters, which is less than those of T.V. signals. On account of smaller wavelength, the microwaves can be transmitted as beam signals in a particular direction, much better than radiowaves because microwaves do not spread or bend around the corners of any obstacle coming in their way. Therefore, microwaves are better carriers of signals than radio waves.

Population covered =\(\rho \times\pi { d }^{ 2 }=\rho \pi 2hR\)
so. \(50\times10^{ 5 }=\rho \times\frac { 22 }{ 7 }\times2\times100\times6.4\times{ 10 }^{ 6 }\)
or \(\rho =\frac { 5\times7 }{ 22\times2\times100\times6.4 } m^{ -2 }\\ \)
\(=\frac { 5\times7\times{ 10 }^{ 6 } }{ 22\times2\times100\times6.4 } \quad km^{ -2 } \ \\=1242.9\ km^{ -2 }\)

AS the range of T.V. transmission, \(d=\sqrt { 2hr } \)so by increasing height of tower \(h\) the distance \(d\) upto which T.V. coverage can be done will increase. That is why to have greater T.V. coverage transmission has to be made using tall antennas.

(a) In the process of modulation, some specific characteristics of the carrier wave is varied in accordance with the information or message signal.
The carrier wave may be :
(i) Continuous (sinusoidal) wave, or
(ii) Pulse, which is discontinuous.
A continuous sinusoidal carrier wave can be expressed as
\(E={ E }_{ 0 }sin\left( \omega t+\phi \right)\)
Three distinct characteristics of such a wave are amplitude (E₀ ), angular frequency \(\left( \omega \right) \)  and phase angle \(\left( \phi \right) \) . Anyone of these three characteristics can be varied in accordance with the modulating baseband (AF) signal, giving rise to the respective amplitude modulation; frequency modulation and phase modulation.
Again, the significant characteristics of a pulse are pulse amplitude, pulse duration or pulse width and pulse position (representing the time of rise or fall of the pulse amplitude). Anyone of these characteristics can be varied in accordance with the modulating baseband (AF)signal, giving rise to the respective, pulse amplitude modulation (PAM), pulse duration modulation (PDM) or pulse width modulation (PWM) and pulse position modulation (PPM).
(b) Amplitude Modulation: When a modulating AF wave is superimposed on a high frequency carrier wave in a manner that the frequency of modulated wave is same as that of the carrier wave, but its amplitude is made proportional to the instantaneous amplitude of the audio frequency modulating voltage, the process is called amplitude modulation (AM).
Let the instantaneous carrier voltage (e_c ) and modulating voltage (em) be represented by
\({ e }_{ c }={ E }_{ c }sin{ \omega }_{ c }t ...(i)\)
\(\\ { e }_{ m }={ E }_{ m }sin{ \omega }_{ m } \quad ...(ii)\)
Thus, in amplitude modulation, amplitude A of modulated wave is made proportional to the instantaneous modulating voltage e_m
\(i.e., A={ E }_{ c }+{ ke }_{ m }\quad ...(iii)\)
where k is a constant of proportionality.
In amplitude modulation, the proportionality constant k is made equal to unity. Therefore, maximum positive amplitude of AM wave is given by
\(A={ E }_{ c }+{ e }_{ m }={ E }_{ c }+{ E }_{ m }\)
\(sin \ { \omega }_{ m }t \ \ ...(iv)\)
It is called top envelope.
The maximum negative amplitude of AM wave is given by
\(-A=-{ E }_{ c }-{ e }_{ m }\)
\(=-\left( { E }_{ c }+{ E }_{ m }sin\ { \omega }_{ m }t \right) ...(v)\)

(a) The ultra-high frequency em radiations, continuously emitted by a mobile phone, may harm the system of the human body.
(b) Sister Anita shown
(i) Concern about her brother
(ii)  Awareness about the likely effects of em radiations on human body
(iii) Sense of responsibility   any two)
(c) The sidebands are
\(({ V }_{ c }+{ \upsilon }_{ m }) \ and \ ({ V }_{ c }-{ \upsilon }_{ m })\)
\(or \  (1000 \  + \  10) \  kHz \  and \  (1000 \  - \  10) \ kHz  \)
\(1010 \ kHz \ and \ 990 \ kHz\)

Original transmission range,
\(d=\sqrt { 2hR } \)
New height, \({ h }^{ \prime }=h+\frac { 21h }{ 100 } =1.21h\)
New transmission range,
\({ d }^{ \prime }=\sqrt { 2{ h }^{ \prime }R } =\sqrt { 2\times 1.21hR } =1.1d\)
% increase in range
\(=\frac { { d }^{ \prime }-d }{ d } \times 100=\frac { \left( 1.1d \right) -d }{ d } \times 100\)= 10%

Here, h = 125 m ;
R = 6400 km = 6.4 x 10⁶ m.
Area covered = \(\pi { d }^{ 2 }=\pi \times 2hR\ \left[ \because \ \sqrt { 2hR } \right] \)
= 3.14 x 2 x 125 x 6.4 x 10⁶
= 5024 x 10⁶ m² = 5024 km²