4.4. Waves

Progressive Waves
- Definition: An oscillation that travels through matter or vacuum, transferring energy without transferring matter.
- Particle Movement: Particles in the medium vibrate but do not move with the wave.
Types of Progressive Waves
- Transverse Waves: Oscillations are perpendicular to wave travel direction (e.g., electromagnetic waves, surface water waves).
  - Characteristics: Peaks and troughs indicate maximum and minimum displacement.
- Longitudinal Waves: Oscillations are parallel to energy transfer direction (e.g., sound waves).
  - Characteristics: Compressions (particles close together) and rarefactions (particles spread out).

Displacement: Distance from equilibrium position.
Amplitude: Maximum displacement from the origin.
Wavelength: Minimum distance between two adjacent points on a wave oscillating in phase.
Period (T): Time for one full oscillation (one wavelength) to pass a point.
Frequency (f): Number of complete oscillations per unit time.
Wave Speed (v): Distance traveled by a wave per unit time.
Phase Difference: Difference in displacement of particles; measured in radians.
- In Phase: Particles oscillate in sync (phase difference is a multiple of 2π).
- Antiphase: Phase difference of π (half a wavelength out of step).
Wave Equation:
- Relationship: v = fλ
- T = 1/f (Period is reciprocal of frequency).

Using an Oscilloscope: Connect a microphone to measure a signal.
- Timebase on x-axis (time), y-axis (amplitude).
- Measure time for full oscillation to find frequency.

Reflection: Change in wave direction at a boundary, remaining in the original medium.
- Example: Light reflecting off a mirror (angle of incident = angle of reflection).
- Wavelength and frequency remain constant.
Refraction: Change in direction due to speed change entering a new medium.
- Frequency remains constant; speed changes (sound waves speed up in dense materials; EM waves slow down).
Diffraction: Spreading of a wave when passing through a gap.
- Maximum diffraction when gap size equals wavelength.
Polarisation: Unique to transverse waves; oscillation restricted to one plane.
- Longitudinal waves cannot be polarised.

Ripple Tank: Demonstrates wave properties using an oscillating paddle.
- Adjust tank depth for refraction, add a slit for diffraction.
Polarization of Visible Light: Use two polarizing filters.
- One filter rotated 90° decreases light intensity to a minimum.
Microwave Polarization: Metal grille used with a microwave transmitter and receiver.
- Vertical grille allows maximum signal; rotating to horizontal reduces signal due to absorption by metal.

Definition: Radiant power passing at right angles through a surface, per unit area.
- Formula: I = P/A (units: W/m²).
Intensity and Distance:
- Light intensity from a point source inversely proportional to the square of the distance (I ∝ 1/r²).
Intensity and Amplitude:
- Intensity is proportional to the square of the amplitude (I ∝ A²).

Electromagnetic Spectrum: Transverse waves, electric and magnetic fields oscillating at right angles, travel through vacuum at speed 3.0 x 10⁸ m/s.
- Visible light is a small part of the spectrum.

Changes in Direction: A ray entering a new medium at an angle is subject to reflection and refraction.
- Refraction occurs with speed changes.
Refractive Index:
- Formula: n = c/v, where n is refractive index, c is speed of light in vacuum, v is speed in the medium.

Conditions: Occurs when light travels from a material with a higher refractive index to one with a lower index and exceeds the critical angle.
Critical Angle Formula: C = 1/n (only true if originating in air).

Principle: When two or more waves meet, they superpose, creating a resultant wave.
- Resultant displacement equal to the sum of displacements of individual waves.
Interference:
- Constructive: Waves in the same direction add together.
- Destructive: Waves in opposite directions cancel each other.

Sound Waves: Use two audio signal generators for coherent waves, forming an interference pattern detected by a microphone with an oscilloscope.
Young's Double-Slit Experiment: Light passes through slits, producing interference pattern.
- Wavelength determined using λ = a/x (a = distance between slits, d = distance to screen).
Diffraction Grating: Interference pattern created with many opaque lines.
- Formula: d sin(θ) = nλ (n = order of maxima).

Formation: Created by two progressive waves with the same frequency, traveling in opposite directions, superposing to create nodes and antinodes.
- Nodes: Zero amplitude; Antinodes: Maximum displacement.
Characteristics: Nodes are half a wavelength apart.
- Stationary waves do not transfer energy; they store it.

Using a Stretched String:
- String held taught, oscillated with a vibration generator to create stationary wave.
Using Microwaves:
- Microwave reflected off a plate, producing stationary wave patterns.
Using Sound in Air Tubes:
- Tuning fork creates sound; tube length adjustments result in stationary wave formation.

Fundamental Frequency: Lowest frequency for a given arrangement, first harmonic.
Higher Frequencies: Alter the vibration patterns to create new harmonics.
**Stationary waves only form at specific frequencies (multiples of fundamental frequency).

Young's Double-Slit Experiment: A fundamental demonstration of the wave nature of light.

Setup: Light is shone through two closely spaced slits onto a screen.
Interference Pattern: Results in a series of bright and dark fringes on the screen, due to constructive and destructive interference of light waves.
Wavelength Determination: Wavelength can be calculated using the formula λ = a/x, where:
- a = distance between the slits
- x = distance from the slits to the screen.
Significance: Demonstrates that light exhibits both wave and particle properties; supports the theory of superposition.