Lecture Notes: Introduction to Transverse Waves

Overview

• Focus on transverse pulses, principle of superposition, constructive and destructive interference.
• Transverse waves require a medium (e.g., air, water).
• Examples: ocean waves, ripples from a stone in a pond.

Transverse Waves

• Composed of a series of pulses.
• Pulse: A single disturbance in a medium.
  • Example: Dropping a stone in water.
• A wave is a series of pulses.

Pulse Characteristics

• Amplitude: Distance from the center to the peak of the pulse.
• Pulse Width: Duration of the pulse.
• Velocity: Speed at which the pulse travels.

Transverse Pulse

• Particles move at right angles to the direction of the pulse.
  • Example: Particles move up and down, while pulse moves left to right.

Principle of Superposition

• Superposition: Algebraic sum of amplitudes of two pulses occupying the same space.
  • Example: Pulse A (2 cm) + Pulse B (1 cm) = 3 cm resultant pulse.
  • After superposition, pulses continue in original directions with original amplitudes.

Types of Interference

Constructive Interference

• When crests of two pulses overlap.
• Results in increased amplitude.
  • Example: Pulse A (2 cm) + Pulse B (2 cm) = 4 cm resultant pulse.

Destructive Interference

• When crest of one pulse overlaps with trough of another.
• Results in reduced amplitude or cancellation.
  • Example: Crest (2 cm) + Trough (2 cm) = 0 cm (cancellation).
• Partial cancellation:
  • Example 1: Crest (6 cm) + Trough (4 cm) = 2 cm resultant pulse.
  • Example 2: Crest (3 cm) + Trough (7 cm) = -4 cm resultant pulse.

Summary

• Constructive interference builds up amplitude.
• Destructive interference reduces or cancels amplitude.
• Pulses retain original direction and amplitude post-superposition.

In the next session, the focus will be on transverse waves.