Comprehensive Study Guide to Waves, Light, and Sound Physics

Fundamental Descriptions of Waves

Essential Wave Distinction:
- Waves are categorized by the relationship between particle oscillation and the direction of energy transfer (also known as the direction of wave travel or wave propagation).
- Longitudinal Waves: Occur when the direction of particle oscillations is parallel to the direction of wave energy transfer.
- Transverse Waves: Occur when the direction of particle oscillations is perpendicular ( $90^{\circ}$ ) to the direction of wave energy transfer.
Key Wave Terminology:
- Time Period ( $T$ ): Defined as the time taken for one complete cycle of the wave to pass a fixed point. Alternatively, it is the time required for a single particle disturbed by the wave to complete one full cycle of oscillation.
- Frequency ( $f$ ): The number of wave cycles passing a fixed point per unit time. If measured in Hertz ( $Hz$ ), frequency represents the cycles per second.
- Mathematical Relationship: Frequency and time period are inversely proportional: $f = \frac{1}{T}$
- Equilibrium/Undisturbed Position: The location of particles before they are disturbed by a wave (e.g., the position of a straight string).
- Amplitude ( $A$ ): The maximum distance a particle moves from its equilibrium position during an oscillation cycle. On a transverse wave, this is the distance from the undisturbed position to a peak (crest).
- Peak/Crest: The points where particles are at their maximum distance above the undisturbed position.
- Trough: The lowest points on a wave cycle, synonymous with the maximum distance below the undisturbed position.
- Wavelength ( $\lambda$ ): The distance in the direction of energy transfer between a specific point on one wave (such as a peak) and the adjacent identical point at the same stage of the oscillation cycle.

Representing Waves: Rays and Wavefronts

Ray Diagrams:
- Rays are drawn as straight lines to represent waves traveling in straight paths.
- Arrows on rays indicate the direction of wave propagation and energy transfer.
Wavefronts:
- A wavefront is constructed by joining all adjacent particles that are currently at a peak.
- Refracted light through water surfaces creates patterns of bright and dark shapes that mirror the wavefronts of underlying water waves.
Interaction Properties:
- The perpendicular distance between adjacent wavefronts is equal to the wavelength ( $\lambda$ ).
- If rays and wavefronts are illustrated together, the rays are always perpendicular to the wavefronts at their intersection points.

Reflection and the Law of Reflection

Universal Application: While mirrors are the primary focus, all waves (including sound waves reflecting off building walls) undergo reflection.
Component Definitions:
- The Normal: An imaginary construct drawn perpendicular to the boundary (mirror) at the exact point where the incident ray strikes it.
- Angle of Incidence ( $i$ ): The angle measured between the incident ray and the normal.
- Angle of Reflection ( $r$ ): The angle measured between the reflected ray and the normal.
The Law of Reflection: States that the angle of incidence is equal to the angle of reflection ( $i = r$ ).

Refraction and Media Interaction

Media and Boundaries:
- Medium (plural: media): Any substance or material through which a wave travels.
- Boundary: The interface where two different media meet (e.g., the surface of a rectangular glass prism).
The Mechanism of Refraction: Refraction is caused by a change in the speed of the wave as it crosses the boundary between media.
- Light Speed Trends: Light travels fastest in a vacuum and nearly as fast in air. It travels slower in liquid and solid media.
- Specific Speed Order (Slowest to Fastest): Glass, Perspex, Water.
Refraction Rules:
- Faster to Slower Medium (e.g., Air to Perspex): The ray bends towards the normal. The angle of refraction ( $r$ ) is less than the angle of incidence ( $i$ ).
- Slower to Faster Medium (e.g., Perspex to Air): The ray bends away from the normal. The angle of refraction ( $r$ ) is greater than the angle of incidence ( $i$ ).
Non-Light Examples: Sound waves refract when crossing layers of air with different temperatures; sound travels slower in colder, denser air compared to hotter, less dense air.

Total Internal Reflection (TIR)

Definition: A phenomenon where all incident light is reflected back into the original medium rather than being refracted across the boundary.
Required Conditions for TIR:
1. The light must be traveling through a medium where its speed is slower than in the medium on the other side of the boundary (it must be attempt to 'speed up').
2. The angle of incidence must be greater than or equal to the Critical Angle.
The Critical Angle: The specific angle of incidence at which the refracted ray would theoretically travel along the boundary ( $90^{\circ}$ refraction). At this angle and above, refraction ceases and total internal reflection occurs.
Practical Applications:
- Fibre Optic Cables: Light is trapped inside a glass 'core' by a faster 'cladding' layer, allowing light to travel around bends via repeated TIR.
- Bicycle Reflectors: Designed with a flat front and a zig-zag back. Light enters perpendicular to the front, hits the zig-zag boundaries at angles greater than the critical angle, undergoes TIR twice, and returns toward the source (e.g., a car driver).

Mechanics of Seeing Objects

Key Processes:
- Emit: To give out or produce light (Luminous objects).
- Reflect: To bounce off a surface without being taken in (Non-luminous objects).
- Absorb: To take in the wave energy.
- Transmit: To pass through a medium without being absorbed.
The Sequence of Sight:
1. A source emits light.
2. Light travels toward the object.
3. Light is reflected by the surface of the object.
4. Reflected light travels to the eye and is transmitted through the air.
5. Light is absorbed by the retina at the back of the eye.
Absorption and Depth: In water, light is both transmitted and absorbed. This explains why it is dark at the bottom of the ocean while light remains visible $10\,m$ below the surface.
Virtual Images and Apparent Depth:
- Mirror Images: Ray diagrams use dashed 'virtual rays' to show where reflected light appears to originate from behind the mirror.
- Apparent Depth: Objects in water appear closer to the surface than they are due to light refracting away from the normal as it moves from water to air. Virtual rays traced back to the eye identify the 'apparent' position of the object (e.g., a fish).

Colour Physics

Spectrum of Light: White light is a mixture of the entire visible spectrum (red, green, blue light and others).
Surface Colour Logic:
- Red Surfaces: Absorb blue and green light; reflect only red light.
- White Surfaces: Contain and reflect all colors of light.
- Black Surfaces: Absorb all colors and reflect no light. They are 'seen' by the contrast with surrounding reflecting surfaces.
Filter Mechanics:
- A red filter absorbs all colors except red, which it transmits.
- If white light passes through a red filter and then a blue filter, no light passes through because the red filter only allows red, and the blue filter absorbs red.
Colour Addition (Mixing Coloured Light):
- $Red + Blue = Magenta$
- $Blue + Green = Cyan$
- $Green + Red = Yellow$

Sound Waves

Production: Sound is produced by vibrating objects and requires a medium (gas, liquid, or solid) to travel through.
Nature of the Wave: Sound waves are longitudinal waves consisting of particle oscillations parallel to the direction of propagation.
- Compressions: High-pressure regions where air particles are closer together than average.
- Rarefactions: Low-pressure regions where air particles are spread further apart.
- Wavelength of Sound: The distance between adjacent compressions.
Perception: We perceive sound frequency as musical pitch. Higher frequency corresponds to a higher pitch.

Investigating Sound with Technology

Microphone: Converts incident sound waves into a time-varying voltage. The frequency of the voltage matches the sound frequency, and the voltage level increases with loudness.
Oscilloscope: Plots a graph (trace) of Voltage vs. Time.
- Trace Characteristics:
  - Horizontal Axis: Represents time. Smaller horizontal distances between peaks indicate a smaller time period, thus a higher frequency/pitch.
  - Vertical Axis: Represents voltage (amplitude). A greater vertical distance from peak to trough indicates a louder sound.
Trace Context (Pure Tones): Pure tones have a constant frequency and no harmonics (zero timbre). Electronic instruments produce pure tones, whereas musical instruments (flutes, violins, pianos) produce complex waves with character (timbre).

Human Hearing and Anatomy

Anatomical Pathway:
1. Auditory Canal: Directs sound waves through the air to the eardrum.
2. Eardrum: Oscillates (moves back and forth) in response to sound waves.
3. Ossicles: Small bones that amplify and pass oscillations to the cochlea.
4. Cochlea: Contains fluid through which sound waves travel. Specialized detection cells convert fluid motion into nerve impulses.
5. Auditory Nerve: Carries nerve impulses from the cochlea to the brain.
Hearing Safety:
- Loudness is measured on the decibel scale ( $dB$ ).
- Protection methods: Rigid materials reflect sound; spongy materials absorb sound.

Quantities, SI Units, and Prefixes

Quantity	Symbol	SI Unit	Unit Symbol
Wavelength	$\lambda$	metres	$m$
Time period	$T$	seconds	$s$
Frequency	$f$	hertz	$Hz$
Wave speed	$v$	metres per second	$m/s$

SI Prefixes ( $10^{3n}$ ):
- Giga ( $G$ ): $10^9$ (e.g., microwave oven frequency: $2.7 \times 10^9\,Hz = 2.7 G\,Hz$ )
- Mega ( $M$ ): $10^6$
- kilo ( $k$ ): $10^3$
- centi ( $c$ ): $10^{-2}$ ( $1/100$ )
- milli ( $m$ ): $10^{-3}$
- micro ( $\mu$ ): $10^{-6}$
- nano ( $n$ ): $10^{-9}$ (e.g., red light wavelength: $0.0000004\,m = 400\,nm$ )

The Wave Equation and Problem Solving

Derivation: Based on the principle that it takes one time period ( $T$ ) for a wave peak to travel one wavelength ( $\lambda$ ). $Speed = \frac{Distance}{Time} \rightarrow v = \frac{\lambda}{T}$ Since $f = \frac{1}{T}$ , then: $v = f \lambda$
Physics Working Standards:
1. State the relationship formula ( $v = f \lambda$ ).
2. Show substitutions including prefix conversion (e.g., $10\,km$ becomes $10 \times 10^3\,m$ ).
3. Calculate and state final answers. Note: For working, scientific notation (e.g., $650 \times 10^{-9}$ ) is used for calculator input.
Mass and Weight Note: When using $W = mg$ , mass must be in kilograms ( $kg$ ).

The Electromagnetic Spectrum

Nature of EM Waves: Transverse waves consisting of oscillating electric fields and magnetic fields oriented perpendicular to each other and to the direction of propagation.
Transmission: Unlike sound, EM waves do not require particles and can travel through a vacuum.
Spectral Regions (Increasing Frequency / Decreasing Wavelength):
1. Radiowaves
2. Microwaves
3. Infra-red radiation
4. Visible light ( $400\,nm$ to $700\,nm$ )
5. Ultra-violet radiation
6. X-rays
7. Gamma rays
Electric Field Definition: A region where a charged particle (proton, electron, or ion) experiences a force. Field strength directly correlates to force magnitude.