Summary Notes - Mechanical Waves

Definition of a Wave: A wave is a disturbance that transfers energy from one place to another (or from place to place) without moving matter over that distance.
Definition of a Medium: A medium is defined as a physical material or matter through which a wave travels.
Four Major Types of Waves:
- Sound waves
- Light waves
- Radio waves
- Water waves

Mechanical Waves:
- Disturbance Mechanism: Transfers energy through physical matter.
- Medium Requirement: Yes, explicitly requires matter to travel.
- Examples: Water waves, sound waves, and seismic waves.
- Primary Structural Subtypes: Transverse waves and longitudinal waves.
Electromagnetic Waves:
- Disturbance Mechanism: Transfers energy through combined electric and magnetic fields.
- Medium Requirement: No medium needed; capable of traveling through a vacuum as well as through matter.
- Examples: Light waves, radio waves, ultraviolet (UV) waves, and X-rays.

Transverse Waves:
- Particle Motion: The particles in the medium vibrate or move perpendicular ( $90^\times$ or at right angles) to the direction that the wave energy travels.
- Physical Metaphor/Example: Holding a piece of rope and rapidly moving a hand up and down to create a snake-like wave pattern.
- Anatomy of Transverse Waves:
  - Crest: The high points or top peaks of a wave.
  - Trough: The low points or bottom valleys of a wave.
  - Rest Position (Midpoint): The baseline position of the medium when no disturbance or energy is passing through it.
Longitudinal Waves:
- Particle Motion: The particles in the medium move and vibrate in the same direction (parallel) as the direction that the wave energy travels.
- Physical Metaphors/Examples: Sound waves propagating through air, or a stretched spring toy (Slinky) pushed and pulled end-to-end.
- Anatomy of Longitudinal Waves:
  - Compression: Regions where the medium's particles come together and are tightly packed.
  - Rarefaction: Regions where the medium's particles spread far apart.

Three Core Mechanical Wave Properties: Amplitude, Wavelength, and Frequency.
Amplitude:
- Definition: The distance measured from the midpoint (rest position) of the wave to its crest, or from the rest position to its trough.
- Energy Relationship: Direct indicator of how much energy a mechanical wave possesses.
- Energy Dynamics: Higher amplitude corresponds to higher energy; lower amplitude corresponds to lower energy.
Wavelength:
- Definition: The physical distance between corresponding points on two consecutive wave cycles.
- Measurement in Transverse Waves: Distance from two consecutive crests or two consecutive troughs.
- Measurement in Longitudinal Waves: Distance from two consecutive compressions or two consecutive rarefactions.
Frequency:
- Definition: The number of complete wavelengths or cycles that pass a given point in a specific timeframe (how often the wave occurs).
- SI Measurement Unit: Measured in Hertz ( $Hz$ ), defined as the number of wavelengths passing a point in $1\text{ second}$ .
- Inverse Wavelength Dynamics:
  - Longer wavelengths correspond to lower frequency.
  - Shorter wavelengths correspond to higher frequency.

Amplitude and Energy Comparison:
- Lower Amplitude Waveform: Exhibits smaller displacement from the rest position and transports lower energy.
- Higher Amplitude Waveform: Exhibits greater displacement from the rest position and transports higher energy.
Wavelength and Frequency Comparison:
- Longer Wavelength Waveform: Exhibits greater distance between consecutive wave cycles and yields a lower frequency.
- Shorter Wavelength Waveform: Exhibits smaller distance between consecutive wave cycles and yields a higher frequency.
Comparative Assessment Across Four Standard Waveforms:
- Highest Amplitude: Waveform $2$ (shows the greatest vertical displacement from rest position).
- Highest Energy: Waveform $2$ (directly resulting from having the maximum amplitude).
- Longest Wavelength: Waveform $3$ (shows the largest horizontal distance between consecutive crests).
- Highest Frequency: Waveform $4$ (shows the maximum number of full wave cycles within a given timeframe).

Amplitude: The distance measured from the midpoint of the wave to the crest (or trough).
Compression: The parts of a longitudinal wave where particles come together and are tightly packed.
Crest: The high points of a wave.
Electromagnetic Wave: Waves that propagate through electric and magnetic fields and do not require any matter through which to travel.
Frequency: How often the wave occurs, measured as the number of full wavelengths passing a point in a given timeframe.
Longitudinal Wave: A wave that travels in the same direction as the movement of the particles in the medium.
Mechanical Wave: A wave that transfers energy through matter.
Medium: The matter or material substance through which a wave travels.
Rarefaction: The parts of a longitudinal wave where particles spread far apart.
Transverse Wave: A wave in which the particles in the wave move perpendicular to the direction that the wave travels.
Trough: The low points of a wave.
Wave: A disturbance that transfers energy from place to place.
Wavelength: The physical distance between one crest to another, or between corresponding points on consecutive waves.