Understand Wave Model — Understand C.2 Wave model - IB Physics

SECTION 1

Historical Context & Motivation

For centuries, scientists debated the fundamental nature of light and sound. Were these phenomena carried by tiny particles flying through space, or were they disturbances rippling through some medium? The answer required a powerful descriptive framework — the wave model. This model provides a unified language for describing how energy travels from one place to another without the permanent displacement of matter itself. From ocean swells to guitar strings to electromagnetic radiation, the wave model ties together an astonishing range of physical phenomena under one set of principles.

1678 • Huygens' Wave Theory of Light

Christiaan Huygens proposed that light travels as a wave through a medium he called the luminiferous aether. His wavefront principle later became essential for explaining diffraction and refraction.

1801 • Young's Double-Slit Experiment

Thomas Young demonstrated interference of light, showing bright and dark fringes that could only be explained if light behaved as a wave.

1864 • Maxwell's Electromagnetic Theory

James Clerk Maxwell unified electricity and magnetism, predicting that light is an electromagnetic wave that requires no medium to propagate.

1924 • de Broglie's Matter Waves

Louis de Broglie proposed that all matter has a wavelength, extending the wave model beyond classical waves to quantum particles.

The central question the wave model answers is deceptively simple: How can energy and information travel across distances without matter itself moving from source to receiver? Understanding how this works — and the mathematical tools that describe it — is the focus of IB Physics topic C.2.

SECTION 2

Core Principles & Definitions

The wave model rests on a few foundational ideas that apply to all types of waves, whether they are mechanical waves in a medium or electromagnetic waves in a vacuum. Grasping these core principles lets you analyse virtually any wave scenario you encounter on the IB exam — or in nature.

Waves Transfer Energy, Not Matter

A wave carries energy from one location to another. The particles of the medium oscillate about their equilibrium positions but do not travel with the wave.

Transverse vs. Longitudinal

In a transverse wave, the oscillation is perpendicular to the direction of energy transfer. In a longitudinal wave, the oscillation is parallel to it.

Key Measurable Quantities

Every wave is described by its wavelength (λ), frequency (f), amplitude (A), and wave speed (v).

Superposition

When two waves meet, their displacements add algebraically — a principle called superposition. This leads to constructive and destructive interference.

Wavefronts & Rays

A wavefront connects points of equal phase. A ray is a line drawn perpendicular to a wavefront, showing the direction of energy transfer.

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KEY TAKEAWAY

Think of a wave like a crowd doing 'the wave' in a stadium. Each person stands up and sits back down in place — no one runs around the stadium. Yet the disturbance (the visual pattern) travels all the way around. That is exactly what a wave does: it moves energy and information across space while the medium's particles simply oscillate about their rest positions.

SECTION 3

Anatomy of a Wave — Visual Explanation

The diagram below shows a snapshot of a transverse wave at a single instant. Study it carefully — most IB wave questions rely on your ability to read amplitude, wavelength, and phase from exactly this kind of graph.

A transverse wave shown as displacement (y) versus position (x). The amplitude A is the maximum displacement from equilibrium. The wavelength λ is the distance between two successive crests (or troughs). Particle oscillation is perpendicular to the wave's direction of travel.

Notice that the crest is the highest point above the equilibrium line, while the trough is the lowest point below it. The vertical distance from equilibrium to either the crest or the trough defines the amplitude, A. The horizontal distance spanning one full cycle — crest to crest, or trough to trough — is the wavelength, λ. These two quantities, along with frequency and wave speed, form the complete description of any periodic wave.

SECTION 4

Mathematical Framework

The wave model is anchored by a small set of elegant equations. Mastering these relationships gives you the tools to solve every C.2 problem on the IB exam.

WAVE EQUATION

v = f × λ

Where v is the wave speed (m s⁻¹), f is the frequency (Hz), and λ is the wavelength (m). This is the most fundamental wave equation.

PERIOD–FREQUENCY RELATIONSHIP

T = 1 / f

The period T (in seconds) is the time for one complete oscillation. It is the reciprocal of frequency.

ANGULAR FREQUENCY & WAVE NUMBER

ω = 2πf k = 2π / λ

ω (angular frequency, rad s⁻¹) tells how rapidly the phase advances in time. k (wave number, rad m⁻¹) tells how rapidly the phase varies across space.

DISPLACEMENT EQUATION (TRAVELLING WAVE)

y(x, t) = A sin(kx − ωt + φ)

This equation gives the displacement y of any particle at position x and time t. φ is the initial phase offset. The minus sign indicates travel in the +x direction.

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IB Exam Tip

Always check your units before substituting. Wavelength should be in metres, frequency in hertz, and speed in m s⁻¹. If wavelength is given in nanometres (nm), convert by multiplying by 10⁻⁹.

SECTION 5

Transverse vs. Longitudinal Waves

The two broad categories of waves — transverse and longitudinal — differ in the relationship between the oscillation direction and the direction of energy transfer. IB Physics expects you to distinguish them clearly, identify real-world examples, and understand which media can support each type.

Top: In a transverse wave, particles oscillate perpendicular to the wave's direction of travel. Bottom: In a longitudinal wave, particles oscillate parallel to propagation, creating regions of compression and rarefaction.

Property	Transverse	Longitudinal
Oscillation direction	Perpendicular to propagation	Parallel to propagation
Can travel through	Solids, surfaces of liquids, vacuum (EM waves)	Solids, liquids, and gases
Can be polarised?	Yes	No
Key examples	Light, radio waves, waves on a rope	Sound, ultrasound, seismic P-waves

Key differences between transverse and longitudinal waves

SECTION 6

Worked Example

Let's apply the wave equation to a typical IB-style problem involving sound in air.

Finding the Wavelength of a Musical Note

1
Step 1 — Identify Given Values

A tuning fork vibrates at a frequency of f = 440 Hz (the note A₄). The speed of sound in air at room temperature is approximately v = 343 m s⁻¹. We need to find the wavelength, λ.
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Step 2 — Select the Appropriate Equation

Use the wave equation: v = f × λ. Rearrange for wavelength: λ = v / f.
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Step 3 — Substitute and Calculate

λ = 343 m s⁻¹ / 440 Hz = 343 / 440 m

λ ≈ 0.780 m
4
Step 4 — Find the Period

Using T = 1 / f: T = 1 / 440 Hz

T ≈ 2.27 × 10⁻³ s (about 2.3 ms)
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Step 5 — Interpret the Answer

The wavelength of the A₄ note is about 78 cm — roughly the length of a guitar. Each oscillation takes about 2.3 milliseconds. This is a longitudinal wave because sound consists of compressions and rarefactions travelling through air.

SECTION 7

Strengths & Limitations of the Wave Model

The wave model is extraordinarily powerful, but like all models in physics, it has boundaries. Understanding where the model excels and where it breaks down will deepen your appreciation of why IB Physics also introduces the particle model of light in later topics.

Strengths	Limitations
Explains reflection, refraction, diffraction, and interference in a unified framework.	Cannot explain the photoelectric effect — light sometimes behaves as particles (photons).
Accurately predicts wavelength, frequency, and speed relationships for all wave types.	Assumes a continuous wave, which fails for very low-intensity light where individual photons matter.
Superposition principle successfully describes complex phenomena like beats and standing waves.	Does not directly account for quantum effects such as energy quantisation.
Works for both mechanical and electromagnetic waves with the same core equations.	For mechanical waves, assumes an ideal medium with no energy loss (real media introduce damping).

Strengths and limitations of the wave model

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KEY TAKEAWAY

Think of the wave model like a road map. A road map is excellent for planning a driving route, showing distances and connections between cities. But it cannot tell you about terrain elevation or building heights — you'd need a topographic map or 3-D model for that. Similarly, the wave model handles propagation, interference, and diffraction beautifully, but when photon-level quantum effects matter, you need the particle model or wave–particle duality.

SECTION 8

Connection to Advanced Wave Phenomena

The concepts in C.2 serve as the foundation for more advanced IB topics, including standing waves, the Doppler effect, and single-slit diffraction. The table below previews how each core idea from this lesson connects to material you will encounter later in the course.

C.2 Foundation	Advanced Application (C.3–C.5)
v = fλ (wave equation)	Used in standing wave harmonics: fₙ = nv / (2L) for strings and pipes.
Superposition principle	Explains constructive / destructive interference patterns in double-slit experiments.
Transverse wave displacement equation	Extended to describe polarisation — restricting the plane of oscillation.
Wavefronts and rays	Foundation for Snell's law, refraction, and Huygens' construction of diffraction.
Frequency and source/observer motion	Leads directly to the Doppler effect equations for sound and light.

How C.2 concepts feed into later IB Physics wave topics

By the end of the IB Physics wave behaviour unit, you will see that every interference pattern, every rainbow, and every musical instrument depends on the handful of principles introduced right here in C.2. Master these fundamentals and the advanced topics will slot naturally into place.

SECTION 9

Practice Problems

Question 1: CONCEPTUAL

A cork is floating on a lake. When a wave passes underneath, the cork bobs up and down but does not move towards the shore. Explain, using the wave model, why the cork stays approximately in the same horizontal position.

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According to the wave model, waves transfer energy, not matter. The water particles oscillate vertically (in this transverse surface wave) about their equilibrium positions. Since there is no net horizontal displacement of the water, the cork does not drift towards the shore. The energy of the wave passes through the cork's location, but the medium (water) and the cork remain in roughly the same place. This demonstrates the key principle that wave propagation is the transfer of a disturbance, not the bulk movement of material.

Question 2: BASIC CALCULATION

A wave on a string has a frequency of 50 Hz and a wavelength of 0.60 m. Calculate (a) the wave speed and (b) the period of the wave.

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(a) Using v = fλ: v = 50 Hz × 0.60 m = 30 m s⁻¹. (b) Using T = 1/f: T = 1/50 = 0.020 s, or 20 ms. The wave speed tells us that each wavefront advances 30 metres every second along the string, and each complete oscillation cycle takes 20 milliseconds.

Question 3: INTERMEDIATE

A sound wave in air (v = 340 m s⁻¹) has a period of 2.50 × 10⁻³ s. Determine the wavelength and the angular frequency of this wave.

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First, find the frequency: f = 1/T = 1 / (2.50 × 10⁻³) = 400 Hz. Then use v = fλ to find wavelength: λ = v/f = 340 / 400 = 0.850 m. For angular frequency: ω = 2πf = 2π × 400 ≈ 2510 rad s⁻¹. This frequency lies near the middle of the audible range. The wavelength of 85 cm reminds us that sound waves often have wavelengths comparable to everyday objects, which is why sound diffracts easily around obstacles.

Question 4: APPLIED

A submarine's sonar emits a pulse at a frequency of 25.0 kHz. The speed of sound in seawater is 1520 m s⁻¹. (a) Find the wavelength of the sonar pulse. (b) If the echo returns in 0.46 s, how far away is the ocean floor?

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(a) Convert frequency: f = 25.0 kHz = 25 000 Hz. λ = v/f = 1520 / 25 000 = 0.0608 m ≈ 6.08 cm. (b) The pulse travels to the ocean floor and back, so the total distance is d_total = v × t = 1520 × 0.46 = 699.2 m. The one-way distance to the ocean floor is 699.2 / 2 ≈ 350 m. This problem illustrates a real-world application of the wave equation — sonar navigation depends entirely on knowing the wave speed and precisely timing echoes.

Question 5: CRITICAL THINKING

Sound cannot travel through a vacuum, but light can. Using the wave model and your knowledge of transverse and longitudinal waves, explain this difference. Then evaluate why the wave model alone is insufficient to fully describe the behaviour of light at very low intensities.

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Sound is a longitudinal mechanical wave — it requires a medium whose particles can compress and rarefy. In a vacuum, there are no particles to oscillate, so sound cannot propagate. Light, however, is a transverse electromagnetic wave consisting of oscillating electric and magnetic fields. These fields do not need a material medium; they sustain each other as described by Maxwell's equations, so light travels freely through empty space. At very low intensities, experiments such as the photoelectric effect reveal that light energy arrives in discrete packets called photons, with energy E = hf. The classical wave model treats light as a continuous wave and cannot explain why a minimum frequency (not intensity) is needed to eject electrons from a metal surface. This is a fundamental limitation of the wave model and is why modern physics adopts wave–particle duality, where light exhibits wave behaviour in some experiments and particle behaviour in others.

SUMMARY

Lesson Summary

Summary

The wave model describes how energy is transferred through oscillations without the permanent displacement of matter. Every wave is characterised by its wavelength (λ), frequency (f), amplitude (A), and wave speed (v), connected by the fundamental relationship v = fλ. Transverse waves oscillate perpendicular to propagation (e.g., light), while longitudinal waves oscillate parallel to it (e.g., sound). Only transverse waves can be polarised.

The superposition principle states that overlapping waves combine by algebraic addition of displacement, producing constructive and destructive interference. The wave model accurately predicts reflection, refraction, and diffraction, but it cannot explain quantum-scale phenomena such as the photoelectric effect, for which the particle model of light is needed. Mastering C.2 provides the essential toolkit for all subsequent IB wave topics.