Definition of Waves and Their Types

Definition of Waves

• A wave is a disturbance that transfers energy and momentum without transporting matter, characterized by oscillation.

Mediums

• Mechanical Waves: Require an elastic medium for energy transfer. Common examples include sound, water waves, and heat.
• Non-mechanical Waves: Do not require a medium. Notable examples include electromagnetic waves (light), radio waves, heat, and x-rays.

Types of Vibration

• Transverse Waves:

  • Vibrate perpendicular to the wave propagation direction.
  • Characterized by crests and troughs.
  • Can only travel through solids with rigidity and can be polarized.

• Longitudinal Waves:

  • Vibrate in the same direction as wave motion.
  • Consist of compressions (areas of high pressure) and rarefactions (areas of low pressure).
  • Can propagate through solids, liquids, and gases; require elasticity but are not polarizable.
  • Examples include sounds produced by instrument strings and disturbances like kinks on a rope.

Propagation of Waves

• Progressive Waves:

  • Move through the medium at a definite velocity, transferring energy. An example is sound waves.

• Stationary Waves:

  • Remain fixed between two boundaries in the medium, with energy confined to specific segments. An example is waves in organ pipes.

Wave Functions

• Wave Pulse: Represents a short-duration disturbance in the medium.
• Wave Function: Expressed as (y = f(x,t)) indicating the wave's dependency on position (x) and time (t).
• An alternate function for wave propagation: (y(t) = f(x ± vt)).

Mathematical Representation

• Equation of Progressive Wave:

  • (y = A \sin(wt + kx)), where (A) is amplitude, (w) is angular frequency, and (k) is the wave number.

• Wave Equation:

  • Describes the relationship between spatial and temporal changes: (\frac{d^2y}{dt^2} = v^2 \frac{d^2y}{dx^2}), where (v) denotes wave speed.