Mechanical Waves Review

Mechanical Waves

• A mechanical wave is a vibration or oscillation that transfers energy and requires a medium (e.g., water, sound, slinky).

Types of Mechanical Waves

• Transverse Waves:

  • Vibration of individuals in the medium is perpendicular to wave propagation.

  • Medium displaced perpendicular to wave direction.

  • Key Features:

  • Crest: Highest point of displacement.

  • Trough: Lowest point of displacement.

• Longitudinal Waves:

  • Vibration of individuals in the medium is parallel to wave propagation.

  • Medium displaced parallel to wave direction.

  • Key Features:

  • Compression: Region where particles are closest together.

  • Rarefaction: Region where particles are more spread out.

• Surface Waves:

  • Displacement is both perpendicular and parallel to wave direction.

• Electromagnetic Waves:

  • Does not require a medium (e.g., light, radio waves, X-rays).

Standing Waves

• Formed when two identical waves travel in opposite directions and interfere in the same medium.

Key Wave Characteristics

Transverse Waves

• Amplitude (A): Displacement from the equilibrium line to the crest or trough.

• Frequency (f): Number of waves passing a given point per second.

• Wavelength ($\lambda$): Shortest distance between repeating points of a wave.

• Wave speed (v): Speed at which a wave travels through a medium, depends only on medium properties.

  • Equation: v = f \lambda

Longitudinal Waves

• Wavelength ($\lambda$) measured between adjacent compressions or rarefactions.

  • Example: An oscillating pendulum producing waves in a medium (spring).

Wave Definitions

• Wave Pulse: A single burst of energy, a one-time disturbance traveling through a medium.

• Wavelength Counting: Count from crest to crest or trough to trough.

Standing Waves: Nodes and Antinodes

• Nodes: Points of no displacement (destructive interference).

• Antinodes: Points of maximum displacement (constructive interference).

Law of Superposition

• Principle that states when two or more waves occupy the same medium, they act independently.

• Constructive Interference: Waves combine to increase amplitude.

• Destructive Interference: Waves combine to decrease or nullify amplitude.

  • Complete Destructive: Complete cancellation.

  • Incomplete Destructive: Partial cancellation.

Wave Phenomena

Interference

• Result of superposition of waves impacting amplitude and position.

Diffraction

• Bending of waves around barriers; effect diminishes as gaps widen.

Refraction

• Bending of waves (e.g., light) as they move from one medium to another.

  • Causes change in speed, wavelength, and direction, while frequency remains constant.

Normal Line

• An imaginary line perpendicular to a surface at a point where a wave hits (e.g., light interacting with a boundary).

Wave Speed Determinants

• Properties of the Medium: Type and characteristics affecting the wave speed.

• Type of Wave: Mechanical vs. electromagnetic.

Constants during Medium Changes

• Constant: Frequency and Energy.

• Changes: Wavelength.

A mechanical wave is a vibration or oscillation that transfers energy and requires a medium (e.g., water, sound, slinky).

Types of Mechanical Waves

Transverse Waves:
Vibration of individuals in the medium is perpendicular to wave propagation.
Medium displaced perpendicular to wave direction.
Key Features:

• Crest: Highest point of displacement.

• Trough: Lowest point of displacement.

Longitudinal Waves:
Vibration of individuals in the medium is parallel to wave propagation.
Medium displaced parallel to wave direction.
Key Features:

• Compression: Region where particles are closest together.

• Rarefaction: Region where particles are more spread out.

Surface Waves:
Displacement is both perpendicular and parallel to wave direction.

Electromagnetic Waves:
Does not require a medium (e.g., light, radio waves, X-rays).

Standing Waves
Formed when two identical waves travel in opposite directions and interfere in the same medium.

Key Wave Characteristics
Transverse Waves

• Amplitude (A): Displacement from the equilibrium line to the crest or trough.

• Frequency (f): Number of waves passing a given point per second.

• Period (T): Time taken for one complete wave to pass a point, inversely related to frequency (T = 1/f).

• Wavelength ($\lambda$): Shortest distance between repeating points of a wave.

• Wave speed (v): Speed at which a wave travels through a medium, depends only on medium properties.
  Equation: v = f \lambda

Longitudinal Waves

• Wavelength ($\lambda$) measured between adjacent compressions or rarefactions.

• Example: An oscillating pendulum producing waves in a medium (spring).

Wave Definitions

• Wave Pulse: A single burst of energy, a one-time disturbance traveling through a medium.

• Wavelength Counting: Count from crest to crest or trough to trough.

Standing Waves: Nodes and Antinodes

• Nodes: Points of no displacement (destructive interference).

• Antinodes: Points of maximum displacement (constructive interference).

Law of Superposition
Principle that states when two or more waves occupy the same medium, they act independently.

• Constructive Interference: Waves combine to increase amplitude.

• Destructive Interference: Waves combine to decrease or nullify amplitude.

  • Complete Destructive: Complete cancellation.

  • Incomplete Destructive: Partial cancellation.

Wave Phenomena

• Interference
  Result of superposition of waves impacting amplitude and position.

• Diffraction
  Bending of waves around barriers; effect diminishes as gaps widen.

• Refraction Bending of waves (e.g., light) as they move from one medium to another.

  • Causes change in speed, wavelength, and direction, while frequency remains constant.

  • When transitioning from less dense to more dense media, wave speed decreases, the wavelength shortens, and the direction of the wave bends towards the normal line.

Normal Line
An imaginary line perpendicular to a surface at a point where a wave hits (e.g., light interacting with a boundary).

Wave Speed Determinants

• Properties of the Medium: Type and characteristics affecting the wave speed.

• Type of Wave: Mechanical vs. electromagnetic.

Constants during Medium Changes

• Constant: Frequency and Energy.

• Changes: Wavelength.