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Study Notes

Unit 2: Waves

Types of Waves

Waves transfer energy from one place to another without transferring matter. There are two primary types based on how particles move relative to the wave's direction of travel:

Transverse Waves: Particles move PERPENDICULAR (at right angles) to the direction the wave travels. Examples: light waves, ripples on water, waves on a guitar string.

Longitudinal Waves: Particles move PARALLEL (back and forth in the same direction) as the wave travels. Example: sound waves in air.

  • Transverse waves have crests (peaks) and troughs (valleys)
  • Longitudinal waves have compressions (squished regions) and rarefactions (spread-out regions)
  • Sound is always a longitudinal wave
  • Light is always a transverse wave

Components of Waves

Transverse wave components:

• Crest: the highest point of the wave above equilibrium

• Trough: the lowest point of the wave below equilibrium

• Amplitude: the distance from the equilibrium (rest) position to a crest or trough — measures the wave's energy/intensity

• Wavelength (λ): the distance between two identical points on consecutive waves (e.g., crest to crest, or trough to trough)

• Equilibrium / rest position: the undisturbed baseline of the medium

Longitudinal wave components:

• Compression: a region where particles are pushed closely together (high pressure)

• Rarefaction: a region where particles are spread apart (low pressure)

Standing wave components:

• Nodes: points of zero displacement (no movement) — where the wave appears stationary

• Antinodes: points of maximum displacement — where the wave moves most

Wave measurements:

• Speed: how fast the wave travels through a medium

• Frequency: how many wave cycles pass a point per second (Hz)

• Period: the time for one complete wave cycle (seconds)

Wave Behaviors

Waves interact with their environment in several ways:

Absorption: The wave's energy is taken in by the medium, reducing the wave's amplitude. Example: Sound is absorbed by foam.

Reflection: The wave bounces off a surface and travels back. Example: Echo of sound off a wall.

Refraction: The wave changes direction when it passes from one medium into another (where speed changes). Example: Light bending through water, creating a straw-in-water optical illusion.

Diffraction: The wave bends and spreads out around obstacles or through openings. Greatest when the opening/obstacle size ≈ wavelength. Example: Sound bending around corners.

Interference: Two or more waves overlap in the same space at the same time.

• Constructive interference: crests align with crests — amplitudes ADD, creating a larger wave

• Destructive interference: crests align with troughs — amplitudes SUBTRACT, reducing or canceling the wave

Doppler Effect: An apparent change in frequency due to relative motion between source and observer. Source moving TOWARD you → higher frequency (higher pitch). Source moving AWAY → lower frequency (lower pitch). Example: ambulance siren changing pitch.

Standing Waves

A standing wave appears to be stationary — it doesn't seem to travel. It is created when a wave and its reflection interfere with each other consistently.

Key features:

• Nodes: fixed points of zero movement (destructive interference zones)

• Antinodes: points of maximum movement (constructive interference zones)

• Number of nodes: the 1st harmonic (fundamental) has 2 nodes (at the ends), 2nd harmonic has 3 nodes, etc.

Note: You will NOT be tested on calculating wavelength of standing waves — only on identifying and counting nodes.

The Double-Slit Experiment

The double-slit experiment demonstrates that light (and other waves) shows wave behavior — specifically, diffraction and interference working together.

How it works:

1. A wave (light) passes through two narrow parallel slits

2. Each slit acts as a new wave source — the waves DIFFRACT (spread out) as they pass through

3. The two diffracted waves then INTERFERE with each other

4. This creates an interference pattern: alternating bright bands (constructive interference, crests + crests) and dark bands (destructive interference, crests + troughs) on a screen

Significance: This result proves light behaves as a wave — a particle would not create this pattern. It was historically important evidence for the wave nature of light.

  • Bright bands = constructive interference (waves reinforce each other)
  • Dark bands = destructive interference (waves cancel each other)
  • Both diffraction AND interference are needed to explain the result
  • The central band is always the brightest