Physics · Textbook solutions

Electromagnetic Waves and Communication System

Every solved example, exercise, and miscellaneous question — in the order the textbook teaches them. · 49 questions

13. Electromagnetic Waves and Communication System — worked examples

9 q

Solved Examples

Worked · 9
  1. Solved Ex.13.1
    Calculate the velocity of EM waves in vacuum.
  2. Solved Ex.13.2
    In free space, an EM wave of frequency 28 MHz travels along the xx-direction. The amplitude of the electric field is E=9.6E = 9.6 V/m and its direction is along the yy-axis. What is amplitude and direction of magnetic field BB?
  3. Solved Ex.13.3
    A beam of red light has an amplitude 2.5 times the amplitude of second beam of the same colour. Calculate the ratio of the intensities of the two waves.
  4. Solved Ex.13.4
    An EM wave of frequency 50 MHz travels in vacuum along the positive xx-axis and E⃗\vec{E} at a particular point, xx and at a particular instant of time t is 9.6 j^9.6\,\hat{j} V/m. Find the magnitude and direction of B⃗\vec{B} at this point xx and at time t.
  5. Solved Ex.13.5
    For an EM wave propagating along xx direction, the magnetic field oscillates along the zz-direction at a frequency of 3×10103 \times 10^{10} Hz and has amplitude of 10−910^{-9} T. a) What is the wavelength of the wave? b) Write the expression representing the corresponding electric field.
  6. Solved Ex.13.6
    The magnetic field of an EM wave travelling along xx-axis is B⃗=k^ 4×10−4sin⁡(ωt−kx)\vec{B} = \hat{k}\,4 \times 10^{-4} \sin (\omega t - kx). Here BB is in tesla, tt is in second and xx is in m. Calculate the peak value of electric force acting on a particle of charge 5 μ\muC travelling with a velocity of 5×1055 \times 10^{5} m/s along the yy-axis.
  7. Solved Ex.13.7
    A radar has a power of 10 kW and is operating at a frequency of 20 GHz. It is located on the top of a hill of height 500 m. Calculate the maximum distance upto which it can detect object located on the surface of the Earth. (Radius of Earth = 6.4×1066.4 \times 10^{6} m)
  8. Solved Ex.13.8
    If the height of a TV transmitting antenna is 128 m, how much square area can be covered by the transmitted signal if the receiving antenna is at the ground level? (Radius of the Earth = 6400 km)
  9. Solved Ex.13.9
    The height of a transmitting antenna is 68 m and the receiving antenna is at the top of a tower of height 34 m. Calculate the maximum distance between them for satisfactory transmission in line of sight mode. (radius of Earth = 6400 km)

Exercises

40 q

Choose the correct option

Practice · 6
  1. 1. Choose the correct option.
    Ex Q.1 (i)
    The EM wave emitted by the Sun and responsible for heating the Earth's atmosphere due to green house effect is
    1. A.
      Infra-red radiation
    2. B.
      X ray
    3. C.
      Microwave
    4. D.
      Visible light
  2. Ex Q.1 (ii)
    Earth's atmosphere is richest in
    1. A.
      UV
    2. B.
      IR
    3. C.
      X-ray
    4. D.
      Microwaves
  3. Ex Q.1 (iv)
    The direction of EM wave is given by
    1. A.
      E⃗×B⃗\vec{E} \times \vec{B}
    2. B.
      E⃗⋅B⃗\vec{E} \cdot \vec{B}
    3. C.
      along E⃗\vec{E}
    4. D.
      along B⃗\vec{B}
  4. Ex Q.1 (v)
    The maximum distance upto which TV transmission from a TV tower of height hh can be received is proportional to
    1. A.
      h1/2h^{1/2}
    2. B.
      hh
    3. C.
      h3/2h^{3/2}
    4. D.
      h2h^{2}
  5. Ex Q.1 (vi)
    The waves used by artificial satellites for communication purposes are
    1. A.
      Microwave
    2. B.
      AM radio waves
    3. C.
      FM radio waves
    4. D.
      X-rays
  6. Ex Q.1 (vii)
    If a TV telecast is to cover a radius of 640 km, what should be the height of transmitting antenna?
    1. A.
      32000 m
    2. B.
      53000 m
    3. C.
      42000 m
    4. D.
      55000 m

Answer briefly

Practice · 25
  1. 2. Answer briefly.
    Ex Q.2 (i)
    State two characteristics of an EM wave.
  2. Ex Q.2 (ii)
    Why are microwaves used in radar?
  3. Ex Q.2 (iii)
    What are EM waves?
  4. Ex Q.2 (iv)
    How are EM waves produced?
  5. Ex Q.2 (v)
    Can we produce a pure electric or magnetic wave in space? Why?
  6. Ex Q.2 (vi)
    Does an ordinary electric lamp emit EM waves?
  7. Ex Q.2 (vii)
    Why do light waves travel in vacuum whereas sound wave cannot?
  8. Ex Q.2 (viii)
    What are ultraviolet rays? Give two uses.
  9. Ex Q.2 (ix)
    What are radio waves? Give its two uses.
  10. Ex Q.2 (x)
    Name the most harmful radiation entering the Earth's atmosphere from the outer space.
  11. Ex Q.2 (xi)
    Give reasons for the following: (i) Long distance radio broadcast uses short wave bands. (ii) Satellites are used for long distance TV transmission.
  12. Ex Q.2 (xii)
    Name the three basic units of any communication system.
  13. Ex Q.2 (xiii)
    What is a carrier wave?
  14. Ex Q.2 (xiv)
    Why high frequency carrier waves are used for transmission of audio signals?
  15. Ex Q.2 (xv)
    What is modulation?
  16. Ex Q.2 (xvi)
    What is meant by amplitude modulation?
  17. Ex Q.2 (xvii)
    What is meant by noise?
  18. Ex Q.2 (xviii)
    What is meant by bandwidth?
  19. Ex Q.2 (xix)
    What is demodulation?
  20. Ex Q.2 (xx)
    What type of modulation is required for television broadcast?
  21. Ex Q.2 (xxi)
    How does the effective power radiated by an antenna vary with wavelength?
  22. Ex Q.2 (xxii)
    Why should broadcasting programs use different frequencies?
  23. Ex Q.2 (xxiii)
    Explain the necessity of a carrier wave in communication.
  24. Ex Q.2 (xxiv)
    Why does amplitude modulation give noisy reception?
  25. Ex Q.2 (xxv)
    Explain why is modulation needed.

Solve the numerical problem

Practice · 9
  1. 2. Solve the numerical problem. Where a value is not stated in the question, take the speed of EM waves in vacuum c=3.0×108c = 3.0 \times 10^{8} m/s (§13.2.2).
    Ex Q.2b (i)
    Calculate the frequency in MHz of a radio wave of wavelength 250 m. Remember that the speed of all EM waves in vacuum is 3.0×1083.0 \times 10^{8} m/s.
  2. Ex Q.2b (ii)
    Calculate the wavelength in nm of an X-ray wave of frequency 2.0×10182.0 \times 10^{18} Hz.
  3. Ex Q.2b (iii)
    The speed of light is 3×1083 \times 10^{8} m/s. Calculate the frequency of red light of wavelength of 6.5×10−76.5 \times 10^{-7} m.
  4. Ex Q.2b (iv)
    Calculate the wavelength of a microwave of frequency 8.0 GHz.
  5. Ex Q.2b (v)
    In a EM wave the electric field oscillates sinusoidally at a frequency of 2×10102 \times 10^{10} Hz. What is the wavelength of the wave?
  6. Ex Q.2b (vi)
    The amplitude of the magnetic field part of a harmonic EM wave in vacuum is B0=5×10−7B_{0} = 5 \times 10^{-7} T. What is the amplitude of the electric field part of the wave?
  7. Ex Q.2b (vii)
    A TV tower has a height of 200 m. How much population is covered by TV transmission if the average population density around the tower is 1000/km2^{2}? (Radius of the Earth = 6.4×1066.4 \times 10^{6} m)
  8. Ex Q.2b (viii)
    Height of a TV tower is 600 m at a given place. Calculate its coverage range if the radius of the Earth is 6400 km. What should be the height to get the double coverage area?
  9. Ex Q.2b (ix)
    A transmitting antenna at the top of a tower has a height 32 m and that of the receiving antenna is 50 m. What is the maximum distance between them for satisfactory communication in line of sight mode? Given radius of Earth is 6.4×1066.4 \times 10^{6} m.