Waves Flashcards
Antinodes
A position of maximum displacement in a stationary wave.
Coherence
Waves with the same frequency and constant phase difference
Diffraction
1. Definition
- The spreading out of waves when they pass through a narrow gap (aperture) or around an obstacle.
- Wavefronts bend at the edges of the gap.
===
2. Key Properties
- Amplitude decreases: Energy dissipates as waves spread.
- Wavelength remains unchanged.
-
Most noticeable when the gap size ≈ wavelength.
- Example: Sound waves (λ ~ cm–m) diffract through doorways, but light (λ ~ nm) requires tiny slits.
===
3. Light Diffraction Patterns
- Single-slit diffraction: Produces alternating bright (constructive interference) and dark (destructive interference) fringes.
- Central maximum: Brightest fringe (all wavelengths combine).
Electromagnetic Waves
Electromagnetic Waves
-
Transverse waves: Consist of perpendicular oscillations:
- Electric field (E)
- Magnetic field (B)
- Travel in vacuum: Unlike mechanical waves, require no medium.
- Universal speed: All EM waves move at c = 3 × 10⁸ m/s in vacuum.
===
Key Behaviors
All EM waves can:
- Reflect (e.g., mirrors for visible light)
- Refract (e.g., lenses bending light)
- Diffract (e.g., radio waves around hills)
- Show polarization (e.g., polarized sunglasses)
- Interfere (e.g., thin-film colors)
Fundamental Mode of Vibration
(1st Harmonic)
- The simplest wave pattern that can form
- Node to Node in closed tube ( L = 1/2 λ)
- Anti-node to anti-node in open tube ( L = 1/2 λ)
- Anti-node to node ( L = 1/4 λ)
- Adding a harmonic adds a node/antinode pair to the tube.
Interference
** Key Definitions**
- Interference: Occurs when waves overlap, combining their displacements.
===
A. Constructive Interference
- Conditions:
- Waves are in phase (peaks align).
- Phase difference: 0, 2π, 4π, …
- Path difference: nλ (where n = 0, 1, 2, …).
- Result:
- Double amplitude (e.g., brighter light, louder sound).
B. Destructive Interference
- Conditions:
- Waves are in anti-phase (peaks align with troughs).
- Phase difference: π, 3π, 5π, …
- Path difference: (n + 1/2)λ.
- Result:
- Zero amplitude (e.g., dark fringes, silence).
===
- Coherence matters: Waves must have the same frequency and stable phase difference.
Nodes
position of minimum displacement in a stationary wave.
Path Difference
- Path difference (Δx): The difference in distance traveled by two waves to reach a point.
- Determines whether interference is constructive or destructive.
===
- Maxima occurs at Constructive Interference
- Minima occurs at Destructive Interference
===
- Verify λ by locating maxima/minima.
Phase
Phase Difference (φ)
-
Definition:
- How far one point’s oscillation cycle is compared to another on the same wave.
-
Phase States:
- In phase: Crests (or troughs) align → 0° or 0 radians.
- Antiphase: Crest aligns with trough → 180° or π radians.
-
Units:
- Degrees (°).
- Radians (rad).
-
Calculations:
- Between two points on the same wave or the same point on two waves with same frequency.
Polarisation
Polarisation
- Definition: The restriction of a transverse wave to oscillate in one plane perpendicular to its direction of propagation.
===
Key Concepts:
-
Transverse Waves Only:
- Occurs in electromagnetic waves (e.g., light) and other transverse waves.
- Impossible for longitudinal waves (e.g., sound), as they oscillate parallel to propagation.
-
How It Works:
- Electric/magnetic fields oscillate in one fixed direction (e.g., vertical or horizontal).
- Vibrations remain perpendicular to energy transfer.
===
Applications & Examples:
- Polaroid sunglasses: Block horizontally polarised glare (e.g., from water).
- LCD screens: Use polarisers to control light.
Progressive Waves
Progressive (Travelling) Waves:
- An oscillation that transfers energy and information through a medium.
- The medium (e.g., water, air) is disturbed, but its particles only oscillate about fixed positions.
- Key feature: Transfers energy without transferring matter.
===
Key Characteristics:
- Energy transfer: Moves energy from one point to another.
- Medium disturbance: Particles vibrate but don’t travel with the wave.
- Wave types: Includes mechanical waves (sound, water) and electromagnetic waves (light, radio).
Reflection
- The bouncing of a wave at a boundary
- The angle of incidence will equal to the angle of reflection
Refraction
1. Definition
- Refraction is the bending of light as it passes from one transparent material (medium) into another with a different density.
- Occurs due to a change in light’s speed between the two materials.
2. Key Observations
-
Bending Direction:
- Toward the normal when entering a denser medium (e.g., air → glass).
- Away from the normal when entering a less dense medium (e.g., glass → air).
- No bending if light enters along the normal (90° to boundary).
- Normal: A dotted line perpendicular to the boundary surface.
- White light splits into a spectrum due to refraction
- Violet light is slowed down more and refracts more than red light
3. What Changes?
- Speed: Slows in denser materials (e.g., glass), speeds up in less dense ones (e.g., air).
- Wavelength: Shortens in denser materials.
- Frequency: Stays constant (colour remains unchanged).
4. Refractive Index (n)
- Measures how much a material slows light:
- Equal to the ratio between the speed of light in a given material, and the speed of light in a vacuum
-
Higher n = denser material
- Always ( n > 1) (light is fastest in vacuum which has n = 1).
Stationary Wave
1. Definition & Formation
- Standing waves are created when two waves with the same frequency, amplitude, and speed travel in opposite directions and superpose.
- Key difference from progressive waves: Standing waves store energy (they do not transfer energy).
===
2. Nodes & Antinodes
-
Nodes:
- Points of zero displacement (no vibration).
- Caused by destructive interference (waves cancel out).
-
Antinodes:
- Points of maximum displacement (peaks and troughs).
- Caused by constructive interference (waves reinforce).
===
-
Phase relationships:
- Points between two nodes are in phase.
- Points separated by an odd number of nodes are out of phase (π radians).
- Points separated by an even number of nodes are in phase (π radians).
===
3. Calculating Wavelength (λ)
- The distance between two adjacent nodes (or antinodes) = λ/2.
Superposition
- When two or more waves of the same frequency meet at a point:
- The resultant displacement = vector sum of individual displacements.
- Occurs for all wave types (sound, light, water, etc.).
Graphical Representation of Wave Superposition
-
Identify Key Points:
- Find where the peaks (maxima) and troughs (minima) of the two waves align.
- Mark points where the waves intersect (zero amplitude).
-
Sum Amplitudes at Each Point:
-
Constructive Interference:
- Peaks align → add amplitudes
-
Destructive Interference:
- Peak meets trough → **subtract amplitudes
-
Partial Interference:
- Non-aligned peaks → vector sum
-
Constructive Interference:
-
Plot the Resultant Wave:
- Connect the summed amplitudes smoothly, maintaining the original wavelength and frequency.
Critical Angle and Total Internal Reflection
1. Critical Angle (C)
- The angle of incidence that produces an angle of refraction of 90°.
- At this angle, the refracted ray travels along the boundary.
2. Total Internal Reflection (TIR)
- Definition: When light cannot exit a denser medium and is fully reflected back.
-
Conditions:
-
Angle of incidence (θ₁) > critical angle (C).
* Light travels from higher n₁ to lower n₂ refractive index (e.g., glass to air).
-
Angle of incidence (θ₁) > critical angle (C).
===
3. Key Points
- No refraction occurs during TIR → all light reflects.
-
Applications:
- Fiber optics: Light signals travel through cables via TIR.
- Diamonds: High critical angle causes brilliant reflections.
Optical density
- The property of a medium that describes how fast light travels through it is called refractive index.
- The more optically dense a material is, the more light slows down when it enters it.
- Refractive index is a measure of this property.
Optical fibre
Total internal reflection in optical fibers for digital signal transmission.
Core with higher refractive index, surrounded by cladding, confines light pulses.
Small core diameter ensures total internal reflection, even around corners.
Optical fibers surpass copper cables due to:
Higher information transmission capacity with light pulses.
Lack of warming during operation, no electrical resistance.
Immunity to external electric and magnetic fields, as light pulses are not charged particles.
Electromagnetic spectrum
Categories & Applications:
- Radio waves (> 0.1 m): Radios, communication.
- Microwaves (0.1 – 1 × 10⁻³ m): Cooking, satellite signals.
- Infrared (1 × 10⁻³ – 7 × 10⁻⁷ m): Thermal imaging, remote controls.
- Visible light (4 × 10⁻⁷ – 7 × 10⁻⁷ m): Human vision, optics.
- Ultraviolet (4 × 10⁻⁷ – 1 × 10⁻⁸ m): Sunbeds, fluorescence.
- X-rays (1 × 10⁻⁸ – 4 × 10⁻¹³ m): Medical imaging.
- Gamma rays (< 1 × 10⁻¹⁰ m): Sterilization, cancer treatment.
===
Key Trends:
- Frequency ↑ → Wavelength ↓ (inverse relationship).
- High frequency = More ionising (e.g., UV, X-rays, gamma rays).
- High wavelength = Greater diffraction (e.g., radio waves bending around obstacles).
===
Energy & Hazard:
- Energy ∝ frequency: Gamma rays (highest energy) are most harmful to cells.
- Ionising radiation damages DNA, increasing cancer risk.
Monochromatic radiation
Electromagnetic wave with only one frequency.
Path difference and phase difference formula
-
distance between waves ÷ wavelength or time difference between waves ÷ time period
(This will give path difference) -
Multipy by 2π
(This gives phase difference)
Red Vs Blue light
- Blue light has a short wavelength and will refract more
- Red light a longer wavelength
Signal Generators & Oscilloscope
Cathode-Ray Oscilloscope (CRO)
- Function: Visualizes voltage changes over time (trace)
-
Trace Types:
- AC: Alternating waveform (positive/negative)
- DC: Flat line at constant voltage
- Audio: Microphone-converted sound waves
-
Controls:
- Vertical (Voltage): Sensitivity dial (V/div)
- Horizontal (Time): Time-base dial (s/div)
-
Measurements:
- Frequency (f = 1/period)
- Peak and peak-to-peak voltage
- Waveform characteristics
-
Signal Generator:
- Produces adjustable waveforms (sine, square, etc.)
- Controls for amplitude, frequency, and shape
- Applications: Electronics testing, oscilloscope input
===
Measurement Principles
-
Time Measurements:
- Use multiple cycles for accuracy
- Critical for frequency calculations
-
Voltage Measurements:
- Peak vs. peak-to-peak
- AC/DC differentiation
-
Unit Conversions:
- Essential for calculations (ms→s, mV→V)
===
Practical Notes
- Always check time-base settings before measurements
- For periodic signals, measure across multiple wavelengths
- Calibrate equipment regularly for accurate readings
Transverse and Longitudinal Waves
Transverse Waves:
- Definition: A wave where particles oscillate perpendicular to the direction of wave travel (and energy transfer).
-
Examples:
- Electromagnetic waves (radio, visible light, UV).
- Waves on a rope.
- Polarisation: Can be polarised.
-
Visual Features:
- Crests: Maximum positive displacement (peaks)
- Troughs: Maximum negative displacement
===
Longitudinal Waves:
- Definition: A wave where particles oscillate parallel to the direction of wave travel (and energy transfer).
-
Examples:
- Sound waves.
- Waves on a slinky spring.
- Polarisation: Cannot be polarised.
-
Visual Features:
- Compressions: High-pressure regions (particles close together)
- Rarefactions: Low-pressure regions (particles spread apart)
General Wave Properties
Displacement (x)
- Distance of a point on the wave from its equilibrium position.
- Vector quantity (can be positive or negative).
Amplitude (A):
- Maximum displacement from equilibrium position.
Wavelength (λ)
- Distance between two in-phase points on successive oscillations.
- Labelling tip: Arrow must go from peak to peak (or trough to trough).
Period (T)
- Time for one complete oscillation.
- Related to frequency:
T = 1/f
Frequency (f)
- Number of complete oscillations per unit time.
- Units: Hertz (Hz) or s⁻¹.
Wave Speed (v):
- Distance travelled per unit time:
v = fλ - Units: m s⁻¹.
===
Diagram Labelling Tips:
-
Wavelength (λ):
- Draw arrows from peak to peak (not mid-points).
-
Amplitude (A):
- Arrow from equilibrium to peak (not trough to peak).
-
Period (T):
- Measure one full cycle on a displacement-time graph
Intensity of a Progressive Wave
Wave Intensity
-
Definition:
- Energy transferred per unit area per unit time
- Intensity (W m⁻²),
- Area perpendicular to wave direction (m²).
-
Key Relationship:
- I ∝ A²
Spherical Waves
-
Behavior:
- Spread equally in all directions from a point source.
- Wavefront area = Surface area of sphere:
A = 4πr²
-
Intensity at Distance ( r ):
I = P / (4πr²)- Follows an inverse square law:
I ∝ 1/r²
- Follows an inverse square law:
===
Key Implications
-
Energy Conservation:
- Total wave power (( P )) remains constant, but spreads over larger areas.
-
Practical Examples:
- Sound from a speaker.
- Light from a star.
Polarising Filters and Metal Grilles
1. Polarisation by Filters
-
When transmission axes are parallel:
- Filter A polarises light in one plane.
- Filter B (parallel) allows maximum intensity through.
-
When transmission axes are perpendicular:
- Filter B blocks all light → minimum intensity (zero).
-
Rotating Filter B:
- Graph of intensity vs. angle shows periodic variation (peaks at 0°, 180°; zero at 90°, 270°). (Cos graph)
2. Polarisation by Reflection/Scattering
- Light can also polarise when:
- Reflected (e.g., glare from water).
- Refracted (e.g., through crystals).
- Scattered (e.g., Rayleigh scattering in the atmosphere).
===
Metal Grilles for Microwaves
1. How They Work
-
Absorb electric fields parallel to grille orientation using free electrons.
- Vertical grille → passes horizontal electric fields.
- Horizontal grille → passes vertical electric fields.
- Key Difference: Grilles absorb aligned fields; polarising filters block them.
2. Experiment: Observing Microwave Polarisation
-
Setup:
- Transmitter emits polarised microwaves (~3 cm wavelength).
- Receiver detects signal (ammeter/loudspeaker).
-
Procedure:
- Rotate receiver → signal peaks (axes aligned) and drops to zero (axes perpendicular).
- Insert metal grille between them:
- Grille parallel to E-field: Blocks all waves (ammeter reads zero).
- Grille perpendicular to E-field: Maximises transmission.
3. Real-World Applications
-
TV/Radio Antennas:
- Must match transmitter’s polarity (horizontal or vertical).
- Incorrect alignment → poor signal.
