Waves: Introduction, Types, and Properties

Wave Definition: A wave is a transfer of energy through a medium from one point to another without carrying matter; it only moves matter as it passes through.
Transverse Wave: Particle motion is perpendicular (at a right angle) to the direction of wave movement. Examples include a vibrating guitar string, electromagnetic waves, or ocean waves.
Longitudinal Wave: Particle motion is parallel (back and forth) to the direction of wave movement. Examples include a Slinky wave when pushed/pulled or sound waves.
Mechanical Waves: These require a physical medium to move (e.g., sound waves).
Electromagnetic (EM) Waves: These do not require a medium and can travel through space.

Amplitude: The maximum displacement from the equilibrium (rest) position, measured in meters ( $m$ ). For a longitudinal wave, high pressure areas are compressions and low pressure areas are rarefactions.
Wavelength ( $\lambda$ ): The distance of one complete wave cycle (e.g., crest to crest or compression to compression), measured in meters ( $m$ ).
Frequency ( $f$ ): The number of waves passing a point in one second, measured in Hertz ( $Hz$ ). Higher frequency corresponds to higher energy.
Period ( $T$ ): The time taken for one full wave to pass a point, measured in seconds ( $s$ ). Relationship: $f = \frac{1}{T}$ .
Wave Speed ( $v$ ): Speed depends on the medium. Formula: $v = \lambda \times f$ .

Nature: Sound is a mechanical, longitudinal, and pressure wave caused by vibrations.
Speed: In air at sea level and $21^{\circ}C$ , the speed of sound is $344\,m \cdot s^{-1}$ . It travels faster in hotter media and denser materials (solids > liquids > gases).
Pitch and Volume: Pitch is determined by frequency; loudness is determined by the wave's amplitude.
Infrasound: Sound frequencies below $20\,Hz$ .
Ultrasound: Sound frequencies above $20\,000\,Hz$ . Used for medical imaging (non-invasive), physical therapy, and breaking kidney stones.
SONAR: Stands for Sound Navigation And Ranging; uses reflected sound waves to determine ocean depth.
Echolocation: Used by animals like bats and dolphins to navigate and form a "picture" of surroundings using sound reflection.

Nature: Consists of varying electric and magnetic fields oscillating at right angles to each other and the direction of travel.
Speed: All EM waves travel at $3 \times 10^8\,m \cdot s^{-1}$ in a vacuum.
Wave-Particle Duality: Light behaves as both a wave and a stream of particles called photons (quanta of light).
Photon Energy: Calculated using $E = h \times f$ or $E = \frac{h \times c}{\lambda}$ , where $h$ (Planck's constant) is $6.626 \times 10^{-34}\,J \cdot s$ .
EM Spectrum (Low to High Energy): Radio Waves, Microwaves, Infrared, Visible light, Ultra-violet, X-ray, Gamma rays.
Ionizing Radiation: Includes ultraviolet, X-rays, and gamma rays; can break molecular bonds and destroy biological tissue.

Principle of Superposition: When two pulses pass through the same medium point simultaneously, the resulting displacement is the sum of their individual effects.
Constructive Interference: Occurs when pulses meet and form a larger disturbance.
Destructive Interference: Occurs when pulses meet to result in a smaller or cancelled disturbance (negative amplitude contribution).

Fill in the statements: - 1. Wave motion parallel to direction: Longitudinal wave. - 2. Maximum upwards displacement in Transverse wave: Crest. - 3. One complete wave cycle: Wavelength. - 4. Wave motion perpendicular to direction: Transverse wave. - 5. Maximum displacement in Longitudinal wave: Compressions or Rarefactions. - 6. Ocean wave example: Transverse wave. - 7. Distance from trough to trough: Wavelength. - 8. Measurement of displacement: Amplitude.
Calculation Problems: - 1. $\lambda = 12\,m$ , $f = 10\,Hz \rightarrow v = 120\,m/s$ - 2. $\lambda = 3\,m$ , $f = 15\,Hz \rightarrow v = 45\,m/s$ - 3. $\lambda = 18\,m$ , $f = 0.5\,Hz \rightarrow v = 9\,m/s$ - 4. $\lambda = 0.5\,m$ , $f = 100\,Hz \rightarrow v = 50\,m/s$