1. Radio Waves

Detailed Description

Radio waves are a type of electromagnetic radiation with wavelengths in the electromagnetic spectrum longer than infrared light. They are used for wireless transmission of sound, data, and video in telecommunications, with frequencies from 3 kHz to 300 GHz.

History

Predicted by James Clerk Maxwell in 1867, experimentally produced by Heinrich Hertz in 1887, and used for communication by Guglielmo Marconi in the 1890s.

Derivation of Formula

The speed of radio waves is the speed of light, derived from Maxwell's equations as c = 1/√(μ0ε0), where μ0 is magnetic permeability and ε0 is electric permittivity of vacuum.

Formula: \( c = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \)

Where: c = speed of radio waves (3 × 10^8 m/s), μ0 = permeability of free space (4π × 10^{-7} H/m), ε0 = permittivity of free space (8.85 × 10^{-12} F/m).

Real-Life Example

Used in broadcasting TV signals to homes via antennas.

Solved Questions

Question 1: Calculate the frequency for a radio wave with wavelength 3 m.

Step 1: Use f = c / λ.

Step 2: f = 3e8 / 3 = 100 MHz.

Question 2: Find the wavelength for frequency 100 MHz.

Step 1: λ = c / f.

Step 2: λ = 3e8 / 1e8 = 3 m.

2. Electromagnetic Spectrum

Detailed Description

The electromagnetic spectrum is the range of all types of EM radiation, including radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. Radio waves occupy the lowest frequency portion.

History

Discovered by various scientists; unified by Maxwell in 1865; radio part by Hertz.

Formula: No specific formula, but energy E = h f, where h is Planck's constant.

Derivation of Formula

From quantum theory, energy of photon E = h f, derived from photoelectric effect and blackbody radiation.

Formula: \( E = h f \)

Where: E = energy, h = Planck's constant (6.626 × 10^{-34} J s), f = frequency.

Real-Life Example

From gamma rays in medical imaging to radio waves in communication.

Solved Questions

Question 1: Energy of a 1 MHz radio wave photon.

Step 1: f = 1e6 Hz.

Step 2: E = 6.626e-34 * 1e6 = 6.626e-28 J.

Question 2: Frequency for E = 6.626e-28 J.

Step 1: f = E / h.

Step 2: f = 6.626e-28 / 6.626e-34 = 1 MHz.

3. Frequency

Detailed Description

Frequency is the number of cycles per second of the radio wave, measured in Hertz. It determines the behavior of the wave in propagation.

History

Concept developed in 19th century; unit named after Hertz.

Derivation of Formula

f = 1 / T, from periodic motion.

Formula: \( f = \frac{1}{T} \)

Where: f = frequency (Hz), T = period (s).

Real-Life Example

FM radio at 88-108 MHz.

Solved Questions

Question 1: Frequency if period is 10^{-6} s.

Step 1: f = 1 / T.

Step 2: f = 1 / 1e-6 = 1 MHz.

Question 2: Period for 1 MHz.

Step 1: T = 1 / f.

Step 2: T = 1 / 1e6 = 1e-6 s.

20. Signal-to-Noise Ratio

Detailed Description

Signal-to-noise ratio (SNR) is the ratio of signal power to noise power, indicating the quality of the radio transmission.

History

Introduced in early radio engineering to measure reception quality.

Derivation of Formula

From power ratios, SNR = P_s / P_n, in dB 10 log10(P_s / P_n).

Formula: \( SNR = 10 \log_{10} \left( \frac{P_s}{P_n} \right) \) dB

Where: P_s = signal power, P_n = noise power.

Real-Life Example

Clear radio reception with high SNR vs static with low SNR.

Solved Questions

Question 1: SNR if P_s = 100 W, P_n = 1 W.

Step 1: Ratio = 100 / 1 = 100.

Step 2: SNR = 10 log10(100) = 20 dB.

Question 2: P_s for SNR = 20 dB, P_n = 1 W.

Step 1: 20 = 10 log10(P_s / 1), log10(P_s) = 2.

Step 2: P_s = 10^2 = 100 W.