07 - Waves and Sound

Chapter Nine: Waves

Fundamental Concepts
- Waves are essential in classical physics, transmitting energy and information without the physical movement of matter.
- Mathematically, waves describe any repeating motion (e.g. pendulum, rotating object).
- In quantum mechanics, the concept of wave-particle duality merges wave and particle theories.
Wave Properties
- Diffraction: Occurs when waves bend around obstacles or spread out after passing through openings.
- Interference: Happens when multiple waves overlap, resulting in a new wave pattern.
Types of Waves
- Mechanical Waves: Require a medium for transmission (e.g. sound, water, seismic waves).
- Electromagnetic Waves: Travel through electric and magnetic fields without a material medium (e.g. light, radio waves, microwaves).
- Matter Waves: Quantum mechanical descriptions of particles like protons and electrons.

Definition: Waves are oscillations repeating in time and space; the medium responsible for oscillation varies.
Common Characteristics:
- Amplitude: Maximum displacement from equilibrium position; different units for different wave types (e.g. meters for water waves).
- Wavelength (λ): Distance to complete one full cycle of vibration, measured between crests/troughs.
- Period: Time taken to complete one vibration.
- Frequency: Number of vibrations per second, measured in Hertz (Hz).
Wave Relationship Equations:
- Velocity (v) related to frequency and wavelength:[ v = f \cdot \lambda ]

Transverse Waves: Motion (amplitude) is perpendicular to propagation direction (e.g. water waves).
Longitudinal Waves: Motion (amplitude) is parallel to propagation direction (e.g. sound waves).

Linear Superposition Principle: Total amplitude is the sum of individual waves.
- Constructive Interference: When overlapping waves reinforce each other, resulting in increased amplitude.
- Destructive Interference: When overlapping waves cancel each other out, reducing overall amplitude.

Standing Waves: Created by the interference of two waves traveling in opposite directions.
- Nodes: Points of no displacement.
- Antinodes: Points of maximum displacement.
Resonance: Occurs when a system vibrates at its natural frequency, leading to large amplitude oscillations.

Properties of Sound: Sound is a longitudinal wave characterized by pressure variations created in the medium.
Speed of Sound: Dependent on medium (e.g. 343 m/s in air at 20°C).
Sound Intensity: Measured in decibels; represents power levels.

Describes the change in frequency perceived by an observer relative to the sound source's motion (approaching = higher frequency, receding = lower frequency).
Applications: Used to measure object motion via reflected waves.

Electromagnetic Spectrum: Describes light and other electromagnetic waves; all travel at the speed of light in vacuum.
Wave Behavior: Light behaves as both a wave and a particle (wave-particle duality).

Reflection: Occurs when light bounces off surfaces; angle of incidence equals angle of reflection.
Refraction: Change in light direction when passing through different media; described by Snell’s Law.

Different wavelengths of light refract at various angles, causing separation of colors (e.g. rainbows).
Higher frequencies (blue light) refract more than lower frequencies (red light).

Occurs when light attempts to pass from a denser medium to a less dense medium and reflects completely when angle of incidence exceeds critical angle.
Utilized in optical fibers.

Light exhibits both wave-like (diffraction/interference) and particle-like (photoelectric effect) properties.
Einstein’s theory introduced photons as quantized packets of energy; energy relates to frequency of light as: [ E = h imes f ]
The photoelectric effect showcased the dependency of ejected electrons' behavior on light frequency rather than intensity.