Waves and fields (as structured in guide)

Waves are disturbances that transfer energy without transferring matter. They fall into two categories: mechanical waves (requiring a medium, like sound) and electromagnetic waves (travelling through vacuum, like light).

Transverse waves have oscillations perpendicular to energy transfer direction (light, water surface waves), while longitudinal waves oscillate parallel to propagation (sound, seismic P-waves).

Key wave properties:

• Amplitude (A): maximum displacement from equilibrium (metres)
• Wavelength (λ): distance between successive corresponding points (metres)
• Frequency (f): oscillations per second (hertz, Hz)
• Period (T): time for one complete oscillation, T = 1/f (seconds)
• Wave speed (v): v = fλ (m/s)

Wave equation: v = fλ connects speed, frequency and wavelength.

Fields represent regions where forces act on objects. Gravitational fields surround masses, causing attractive forces (F = GMm/r²). Electric fields surround charges, exerting forces on other charges (F = kq₁q₂/r²). Magnetic fields arise from moving charges or magnets, affecting moving charges with force F = BIL.

Field lines visualize field strength and direction: density indicates strength, arrows show force direction on positive test charges/masses. Equipotential surfaces connect points of equal potential, always perpendicular to field lines.

Wave phenomena include:

• Reflection: bouncing off surfaces (angle of incidence = angle of reflection)
• Refraction: bending at boundaries due to speed change (Snell's law: n₁sinθ₁ = n₂sinθ₂)
• Diffraction: spreading through gaps/around obstacles
• Interference: superposition creating constructive (crest+crest) or destructive (crest+trough) patterns
• Polarization: restricting transverse wave oscillations to one plane

Understanding waves through everyday analogies: Imagine stadium crowds doing "the wave"—people stand then sit, energy travels around the stadium, but individuals stay in their seats. This perfectly illustrates energy transfer without matter transfer.

Electromagnetic spectrum applications: Radio waves (wavelengths ~1m-1km) enable wireless communication; microwaves (~1mm-1m) heat food by exciting water molecules; infrared (~700nm-1mm) is used in night vision and remote controls; visible light (400-700nm) enables vision; UV (~10-400nm) sterilizes equipment but damages skin; X-rays (~0.01-10nm) penetrate soft tissue for medical imaging; gamma rays (<0.01nm) treat cancer through radiotherapy.

Gravitational fields in action: GPS satellites experience weaker gravity at altitude, causing their clocks to run faster (general relativity). Without corrections, GPS would accumulate 10km errors daily! Ocean tides result from the Moon's gravitational field creating differential forces across Earth—closer water experiences stronger pull, creating tidal bulges.

Electric fields everywhere: Lightning demonstrates massive potential differences (~100 million volts) between clouds and ground. When field strength exceeds air's breakdown value (~3×10⁶ V/m), electrons cascade, creating visible discharge paths. Electrostatic precipitators in power plants use strong electric fields to remove ash particles from smoke, reducing pollution.

Magnetic field applications: MRI scanners use powerful magnetic fields (1.5-3 Tesla) to align hydrogen nuclei in body tissues, then detect radio-frequency emissions as nuclei relax. Maglev trains exploit magnetic repulsion to levitate above tracks, eliminating friction and enabling speeds exceeding 600 km/h.

Wave interference: Noise-cancelling headphones detect incoming sound waves and generate opposite-phase waves, creating destructive interference that silences ambient noise—a practical application of superposition principles.

Memory aid: "Radio Mikes Inspire Visible Ultraviolet X-ray Guns" for increasing frequency order.

Example 1: Wave Calculations

Question: A wave travels at 340 m/s with frequency 256 Hz. Calculate wavelength and period.

Solution: Using v = fλ: λ = v/f = 340/256 = 1.33 m

Using T = 1/f: T = 1/256 = 3.91 × 10⁻³ s or 3.91 ms

Examiner note: Always show formula rearrangement. Include units in final answers (1 mark penalty if omitted).

Example 2: Refraction Problem

Question: Light enters glass (n=1.52) from air at 40°. Calculate refraction angle.

Solution: Apply Snell's law: n₁sinθ₁ = n₂sinθ₂

1.00 × sin(40°) = 1.52 × sin(θ₂)

0.643 = 1.52 × sin(θ₂)

sin(θ₂) = 0.643/1.52 = 0.423

θ₂ = sin⁻¹(0.423) = 25.0°

Examiner note: Light slows entering denser medium, bending toward normal. Show all calculation steps for method marks.

Example 3: Gravitational Field

Question: Calculate gravitational field strength at Earth's surface (M=6.0×10²⁴ kg, R=6.4×10⁶ m, G=6.67×10⁻¹¹ Nm²/kg²).

Solution: g = GM/R²

g = (6.67×10⁻¹¹ × 6.0×10²⁴)/(6.4×10⁶)²

g = (4.0×10¹⁴)/(4.1×10¹³)

g = 9.76 N/kg (or m/s²)

Examiner note: Field strength equals acceleration due to gravity. Verify units (N/kg ≡ m/s²). Standard value ~9.81 N/kg; slight variations acceptable.

Example 4: Electric Field Force

Question: Two charges, +3.0 μC and -2.0 μC, separated by 0.15 m. Calculate force magnitude (k=9.0×10⁹ Nm²/C²).

Solution: F = kq₁q₂/r²

F = (9.0×10⁹ × 3.0×10⁻⁶ × 2.0×10⁻⁶)/(0.15)²

F = (5.4×10⁻²)/(2.25×10⁻²)

F = 2.4 N (attractive)

Examiner note: Opposite charges attract. Always convert units (μC to C) before calculating.