IB Physics: Waves Study Guide

Vocabulary: Wavelength

The distance between corresponding points on successive waves

Vocabulary: Crest

The highest point of a transverse wave

Vocabulary: Trough

The lowest point of a transverse wave

Vocabulary: Amplitude

The maximum displacement from the equilibrium position

Vocabulary: Compression

Region in a longitudinal wave where particles are closest together

Vocabulary: Rarefaction

Region in a longitudinal wave where particles are furthest apart

Vocabulary: Medium

The material through which a wave travels

Vocabulary: Oscillation

Repetitive motion back and forth around an equilibrium position

Vocabulary: Frequency

The number of oscillations per unit time

Vocabulary: Time Period

The time taken for one complete oscillation

Vocabulary: Longitudinal Wave

Wave where particle displacement is parallel to the direction of energy transfer

Vocabulary: Transverse Wave

Wave where particle displacement is perpendicular to the direction of energy transfer

Vocabulary: Mechanical Wave

A wave that requires a medium to travel (e.g., sound)

Vocabulary: Electromagnetic Wave

A wave that can travel through a vacuum (e.g., light)

Vocabulary: Standing Wave

A wave formed by the superposition of two travelling waves of equal frequency and amplitude moving in opposite directions

Vocabulary: Node

A point of zero amplitude on a standing wave

Vocabulary: Antinode

A point of maximum amplitude on a standing wave

Vocabulary: Resonance

When a system is driven at its natural frequency, resulting in maximum amplitude

Vocabulary: Driving Frequency

The frequency of the external periodic force applied to a system

Vocabulary: Natural Frequency

The frequency at which a system oscillates freely without external forces

Vocabulary: Damping

The dissipation of energy in an oscillating system

Vocabulary: Light Damping

Amplitude decreases gradually over time; oscillations continue

Vocabulary: Heavy Damping

System returns to equilibrium slowly without oscillating

Vocabulary: Critical Damping

System returns to equilibrium as quickly as possible without oscillating

Vocabulary: Interference

The result of superposing two or more waves

Vocabulary: Constructive Interference

When waves add up to make a larger amplitude

Vocabulary: Destructive Interference

When waves add up to make a smaller (or zero) amplitude

Vocabulary: Reflection

The bouncing back of a wave from a boundary

Vocabulary: Refraction

The change in direction of a wave as it passes from one medium to another

Vocabulary: Diffraction

The spreading of waves as they pass through an aperture or around an obstacle

Vocabulary: Refractive Index

Ratio of speed of light in vacuum to speed of light in the medium

Vocabulary: Phase

The position of a point in time on a cycle of a waveform

Vocabulary: Critical Angle

The angle of incidence for which the angle of refraction is 90 degrees

Vocabulary: Reference Frame

A coordinate system used to measure velocity and position (relevant for Doppler)

Vocabulary: Doppler Effect

Change in frequency/wavelength due to relative motion between source and observer

Vocabulary: Redshift

Increase in wavelength (decrease in frequency) when source moves away

Vocabulary: Blueshift

Decrease in wavelength (increase in frequency) when source moves closer

Syllabus: Sound Properties

Sound is a longitudinal, mechanical wave

Syllabus: Light Properties

Light is a transverse, electromagnetic wave

Syllabus: EM vs Mechanical

EM waves do not need a medium; Mechanical waves do

Syllabus: Standing Wave Phase

Points between two adjacent nodes are in phase

Syllabus: Standing Wave Amplitude

Amplitude varies from zero at nodes to maximum at antinodes

Syllabus: Resonance Cause

Caused when driving frequency equals natural frequency

Syllabus: Effect of Damping on Resonance

Damping reduces the maximum amplitude at resonance

Syllabus: Effect of Damping on Frequency

Damping slightly lowers the resonant frequency

Syllabus: Wavefronts vs Rays

Rays are perpendicular to wavefronts

Syllabus: Ray Behavior

Rays show the direction of energy transfer

Syllabus: Total Internal Reflection Condition 1

Ray must travel from higher refractive index to lower refractive index

Syllabus: Total Internal Reflection Condition 2

Angle of incidence must be greater than the critical angle

Syllabus: Coherent Sources

Sources must maintain a constant phase difference

Data Booklet: v

Symbol for velocity of a wave

Data Booklet: f

Symbol for frequency

Data Booklet: λ

Symbol for wavelength

Data Booklet: T

Symbol for period

Data Booklet: c

Symbol for speed of light

Data Booklet: n

Symbol for index of refraction (in Snell's Law)

Data Booklet: n (Interference)

Symbol for a counting number (integer 1, 2, 3...)

Data Booklet: s

Symbol for distance between interference fringes

Data Booklet: D

Symbol for distance to the screen

Data Booklet: d

Symbol for slit separation

Data Booklet: Units for v

m/s

Data Booklet: Units for c

m/s

Data Booklet: Units for f

Hz or 1/s

Data Booklet: Units for T

Seconds (s)

Data Booklet: Units for n (Refractive Index)

Unitless ratio

Data Booklet: Units for n (Interference)

Unitless counting number

Data Booklet: Units for Angles (theta)

Degrees

Data Booklet: Units for s

Meters (m)

Data Booklet: Units for D

Meters (m)

Data Booklet: Units for d

Meters (m)

Equation: Wave Speed (General)

v = fλ

Equation: Wave Speed (Period)

v = λ / T

Equation: Snell's Law (Indices)

n₁ / n₂

Equation: Snell's Law (Angles)

sin(θ₂) / sin(θ₁)

Equation: Snell's Law (Velocities)

v₂ / v₁

Equation: Snell's Law (Full)

n₁/n₂ = sin(θ₂)/sin(θ₁) = v₂/v₁

Equation: Constructive Interference Path Difference

Path Difference = nλ

Equation: Destructive Interference Path Difference

Path Difference = (n + ½)λ

Equation: Double Slit Fringe Spacing

s = λD / d

Equation: Doppler Effect (Frequency)

Δf / f ≈ v / c

Equation: Doppler Effect (Wavelength)

Δλ / λ ≈ v / c

Equation Condition: Doppler v

v is the relative velocity between observer and source

Equation Condition: Doppler c

c is the speed of the wave (usually light)

Diagram: Normal Line

The dotted line perpendicular to the boundary surface

Diagram: Angle of Incidence

Measured between the Incident Ray and the Normal

Diagram: Angle of Refraction

Measured between the Refracted Ray and the Normal

Diagram: Incident Ray

The arrow pointing towards the boundary

Diagram: Refracted Ray

The arrow pointing away from the boundary into the new medium

Diagram: Medium 1 vs Medium 2

Shows light passing from one material to another

Diagram: Double Slit Source

Monochromatic coherent light wave

Diagram: Diffraction Circular Waves

Shown expanding from the single slit

Diagram: Wave Interference Pattern

Overlapping arcs after the two slits

Diagram: Optical Screen

Where the interference pattern is viewed

Diagram: Fringes

The light and dark bands on the screen

Diagram: 2λ Path Difference

Leads to a bright fringe (constructive)

Diagram: λ Path Difference

Leads to a bright fringe (constructive)

Diagram: 0λ Path Difference

Leads to the central bright maximum

Variable Relationship: n vs v

If Refractive Index (n) increases, Velocity (v) decreases (Inverse)

Variable Relationship: n vs theta

If Refractive Index (n) increases, Angle (θ) decreases (Inverse/bending towards normal)

Variable Relationship: s vs λ

If Wavelength (λ) increases, Fringe Spacing (s) increases (Direct)