Ch 8 – Mechanical Waves - SMO

Mechanical Waves

Wave Terminology

  • Water motion is mostly vertical, not in the direction of the wave.

  • Wave properties:

    • Crest: highest point

    • Trough: lowest point

    • Amplitude: greatest displacement (up/down)

    • Wavelength ( λ): distance of a complete cycle (e.g., crest to crest).

Wave Generation

  • Waves require energy applied to a medium.

  • Can arise from a point source (e.g., pebble drop) or a straight line source (e.g., stick drop).

  • Incident wave: moves toward a barrier.

  • Reflected wave: moves away from a barrier.

  • Wave train: several waves following one another.

  • Similar wave points in phase (e.g., two troughs).

Types of Waves

Transverse Waves

  • Amplitude is perpendicular to wave motion.

  • A pulse is either crest or trough.

  • Transmits pulses without energy loss.

  • Reflected pulse is inverted compared to incident pulse.

Longitudinal Waves

  • Formed by compression and rarefaction.

Universal Wave Equation

  • Relationship: v = fλ (speed = frequency × wavelength).

  • Speed changes when entering a new medium; wavelength ratio remains consistent for constant frequency.

Superposition and Interference

  • Interference occurs when two pulses overlap.

    • Constructive interference: crests/troughs overlap, greater amplitude.

    • Destructive interference: crest and trough cancel out, medium appears at rest.

  • Displacement at interference point equals the algebraic sum of individual pulses.

Standing Waves & Resonance

  • Identical wave trains create a standing wave; appears motionless.

  • Nodes: motionless points; Antinodes: crests/troughs.

  • Full wavelength: 2 complete antinodes or distance between 1 node and 2 nodes away.

Resonating Air Columns

Closed-Tube Resonance

  • Resonates at frequencies related to tube length (¼ λ for the first resonance, fundamental frequency).

Open-Tube Resonance

  • Similar principle; fundamental frequency occurs at half the wavelength.

Doppler Effect

  • Sound frequency changes based on the motion of the source or listener (e.g., car siren).

  • Calculate Doppler frequency: speed affects what is heard; denominator adjustments depend on movement direction.