Wave Behaviour

Q: What is the difference between a wave pulse and a periodic wave?

A pulse is a single, one-off disturbance with no wavelength or frequency because nothing repeats. A periodic wave is a continuous train of identical pulses, repeating in both space (wavelength) and time (period).

Q: Why isn't amplitude the same as the peak-to-peak distance?

Amplitude $x_0$ is the maximum displacement from equilibrium in one direction. Peak-to-peak distance is double that, since it spans from the highest point to the lowest point. Mixing these up causes factor-of-two errors.

Q: Why does frequency stay the same during refraction?

Frequency is set entirely by the source, not the medium. Since $v=f\lambda$ and speed changes at the boundary while frequency can't, wavelength must change instead to keep the equation balanced.

Q: When can total internal reflection actually happen?

Only when light travels from a slower (optically denser, higher-$n$) medium into a faster (lower-$n$) medium, and only when the angle of incidence exceeds the critical angle given by $\sin\theta_c=n_2/n_1$.

Q: Why can sound waves not be polarized?

Sound is a longitudinal wave, oscillating parallel to its direction of travel, so there's no perpendicular plane to restrict. Only transverse waves, which oscillate perpendicular to travel direction, can be polarized.

Q: How do I know if a Doppler-shifted frequency should be higher or lower?

Use the physical rule as a sanity check before trusting algebra: an approaching source always produces a higher observed frequency, and a receding source always produces a lower one.

IB DP Physics Theme C essentials: wave model, standing waves, refraction, diffraction and Doppler shift in one teaser.

Diagram of a transverse wave labelled with wavelength, amplitude and period, alongside a standing wave showing nodes and antinodes

Subject

Physics

Curriculum

IB Diploma Programme

Grade

Topic

Wave Behaviour

Reading

6 min

Difficulty

Standard

Quick facts

Difficulty

★★★☆☆

Exam weight

~15–18% of SL marks (Theme C) + Paper 3 links

Prerequisites

SHM basics, trigonometry, algebra

You'll learn

Wave model, standing waves, refraction, diffraction, Doppler effect

Revision time

25 min

Wave Behaviour is one of the highest-yield topics in IB DP Physics, showing up across Paper 1, Paper 2, and even data-based Paper 3 questions. At its core, every wave transfers energy without transferring matter — and once you master the vocabulary (wavelength, frequency, period, amplitude) and the equation $v = f λ$ , everything else builds on that foundation. This teaser covers the five ideas examiners test most: describing waves correctly, standing waves and the notorious node-spacing trap, refraction and total internal reflection, diffraction with interference and polarization, and the Doppler effect. Each concept comes with the exact common mistakes IB students make and the sanity checks examiners expect you to show. For the full depth — every derivation, worked example, and boundary-condition table — head to the complete RevisionPrep notes linked below.

What you’ll be able to do

✓Define wavelength, frequency, period and amplitude precisely

✓Apply $v=f\lambda$ and $T=1/f$ to travelling waves

✓Distinguish transverse from longitudinal waves and their properties

✓Explain how standing waves form and locate nodes and antinodes

✓Apply Snell's law and calculate the critical angle for total internal reflection

✓Use the double-slit and diffraction grating equations correctly

✓State and apply Malus's law for polarized light

✓Calculate Doppler-shifted frequencies for approaching and receding sources

Wave Model: Describing Any Wave

A periodic wave repeats in space (wavelength, $λ$ ) and in time (period, $T$ ), linked by $v = f λ$ and $T = 1/ f$ . Amplitude $x_{0}$ is the maximum displacement from equilibrium — not the peak-to-peak distance, which is double the amplitude. Wave speed describes how fast the pattern moves, which is completely different from how fast an individual particle in the medium oscillates.

Comparison diagram of a transverse wave and a longitudinal wave showing oscillation directions relative to energy travel

Feature	Transverse waves	Longitudinal waves
Oscillation direction	Perpendicular to travel direction	Parallel to travel direction
Can be polarized?	Yes	No
Example	Light, water surface waves	Sound in air

Exam tip

Always check which wave and which medium a question describes before choosing a speed value — sound in air is not the speed of light.

Common mistake

Using $c = 3.00 \times 1 0^{8}$ m s⁻¹ for a sound wave problem just because it's the 'default' speed constant.

Mini summary

Wave speed is fixed by the medium, frequency by the source, and wavelength adjusts via $v = f λ$ .

Superposition & Standing Waves

When waves overlap, the resultant displacement is the vector sum of each individual displacement — the principle of superposition. A standing wave forms when two identical waves travel in opposite directions and superpose continuously, such as a wave and its own reflection on a fixed string. Unlike a travelling wave, a standing wave transfers no net energy along its length; energy stays trapped, oscillating between kinetic and potential at the antinodes.

Standing wave pattern on a string with nodes and antinodes labelled and the lambda/2 spacing marked

Exam tip

Describing a standing wave needs two separate statements for full marks: amplitude varies with position (zero at nodes, maximum at antinodes) AND there is no net energy transfer along the wave.

Common mistake

Calling the node-to-node (or antinode-to-antinode) distance 'one wavelength' — it's always $λ /2$ . A full wavelength spans node–antinode–node–antinode–node.

Mini summary

Nodes are permanent zero displacement; antinodes oscillate at maximum amplitude; adjacent nodes/antinodes are always $λ /2$ apart.

Refraction, Snell's Law & Total Internal Reflection

Refraction happens because wave speed changes at a boundary while frequency (set by the source) stays fixed, forcing wavelength to change. Refractive index $n = c / v$ compares light's speed in vacuum to its speed in a medium — higher $n$ means slower speed and bending towards the normal. Total internal reflection can only occur travelling from a slower (denser) medium into a faster one, and only above the critical angle.

$Ray diagram showing light refracting at a boundary between two media and total internal reflection at the critical angle$

Exam tip

Sanity-check any critical angle answer: $sin θ_{c}$ must come out less than 1. If it's greater than 1, you've inverted the ratio $n_{2} / n_{1}$ .

Common mistake

Writing $sin θ_{c} = n_{1} / n_{2}$ instead of $n_{2} / n_{1}$ , giving an impossible value greater than 1.

Mini summary

Speed and wavelength change at a boundary; frequency never does. TIR needs slow-to-fast travel plus angle above critical.

Diffraction, Interference & Polarization

Diffraction is the spreading of a wave through a gap or around an edge, most noticeable when the gap width is comparable to the wavelength. In Young's double-slit setup, coherent light diffracts at each slit and the resulting wavelets interfere, giving fringe spacing $s = \frac{λ D}{d}$ ; a diffraction grating extends this with $nλ = d sin θ$ . Only transverse waves can be polarized, and Malus's law $I = I_{0} cos^{2} θ$ gives the transmitted intensity through a second polarizer.

Double slit interference pattern diagram with path difference labelled and a polarizer diagram showing angle theta between transmission axes

Exam tip

For grating questions, find slit spacing $d$ from 'lines per mm' by taking the reciprocal ( $d = 1/ N$ ) and converting to metres before substituting.

Common mistake

Forgetting to convert nanometres and millimetres to metres before using $s = λ D / d$ , or using $cos θ$ instead of $cos^{2} θ$ in Malus's law.

Mini summary

Diffraction spreads waves at gaps; interference from coherent sources builds fringe patterns; polarization only works on transverse waves.

The Doppler Effect

When a source and observer move relative to each other, the observed frequency differs from the emitted frequency because wavefronts bunch up as the source approaches and stretch out as it recedes. For a source approaching a stationary observer, $f^{'} = f (\frac{v}{v - u _{s}})$ ; for a receding source, $f^{'} = f (\frac{v}{v + u _{s}})$ . The same bunching/stretching logic extends to light, giving the approximation $\frac{Δ f}{f} \approx \frac{Δ λ}{λ} \approx \frac{v}{c}$ .

Diagram of Doppler effect showing compressed wavefronts ahead of a moving source and stretched wavefronts behind it

Exam tip

Before trusting your algebra, sanity-check the direction: approaching source means higher observed frequency, receding means lower.

Common mistake

Using $(v + u_{s})$ for an approaching source, which produces a lower frequency than emitted — physically backwards.

Mini summary

Approaching sources raise observed frequency, receding sources lower it; the same principle underlies redshift and blueshift in light.

Quick formula sheet

v = f λ

Wave speed equals frequency times wavelength — Speed = how fast pattern moves; f and λ trade off to keep v constant in a given medium

T = \frac{1}{f}

Period is the reciprocal of frequency

n = \frac{c}{v}

Refractive index compares speed of light in vacuum to speed in the medium

n_{1} sin θ_{1} = n_{2} sin θ_{2}

Snell's law relating angles of incidence and refraction at a boundary

sin θ_{c} = \frac{n _{2}}{n _{1}}

Critical angle for total internal reflection, only valid travelling slow-to-fast medium — Result must be < 1 — if not, you inverted the ratio

nλ = d sin θ

Diffraction grating condition for bright fringes (maxima)

s = \frac{λ D}{d}

Young's double-slit fringe spacing on a distant screen

I = I_{0} cos^{2} θ

Malus's law: transmitted intensity through a second polarizer — Intensity ∝ amplitude² ∝ cos²θ — always square it

f^{'} = f (\frac{v}{v - u _{s}})

Observed frequency for a source approaching a stationary observer

f^{'} = f (\frac{v}{v + u _{s}})

Observed frequency for a source receding from a stationary observer

Practice questions

Easy

A wave has frequency 250 Hz and wavelength 1.2 m. Calculate its speed.
State two differences between transverse and longitudinal waves.
Define wavelength and amplitude for a periodic wave.

Medium

A sound wave in air (v = 340 m s⁻¹) has frequency 500 Hz. Determine its wavelength, and explain why the speed of light must not be used here.
A standing wave on a string has nodes 0.30 m apart. Determine the wavelength of the wave.
Light travels from water ( $n = 1.33$ ) into air. Calculate the critical angle for total internal reflection.

Challenge

Monochromatic light of wavelength 550 nm passes through a diffraction grating with 400 lines per mm. Determine the angle of the first-order maximum.
A car horn emits sound at 500 Hz while the car moves towards a stationary observer at 25 m s⁻¹ (speed of sound = 340 m s⁻¹). Calculate the frequency heard, and explain how you would sanity-check your answer.
Explain, using the principle of superposition, why a standing wave transfers no net energy along its length while still storing energy locally.

Frequently asked questions

What is the difference between a wave pulse and a periodic wave?+

A pulse is a single, one-off disturbance with no wavelength or frequency because nothing repeats. A periodic wave is a continuous train of identical pulses, repeating in both space (wavelength) and time (period).

Why isn't amplitude the same as the peak-to-peak distance?+

Amplitude $x_{0}$ is the maximum displacement from equilibrium in one direction. Peak-to-peak distance is double that, since it spans from the highest point to the lowest point. Mixing these up causes factor-of-two errors.

Why does frequency stay the same during refraction?+

Frequency is set entirely by the source, not the medium. Since $v = f λ$ and speed changes at the boundary while frequency can't, wavelength must change instead to keep the equation balanced.

When can total internal reflection actually happen?+

Only when light travels from a slower (optically denser, higher- $n$ ) medium into a faster (lower- $n$ ) medium, and only when the angle of incidence exceeds the critical angle given by $sin θ_{c} = n_{2} / n_{1}$ .

Why can sound waves not be polarized?+

Sound is a longitudinal wave, oscillating parallel to its direction of travel, so there's no perpendicular plane to restrict. Only transverse waves, which oscillate perpendicular to travel direction, can be polarized.

How do I know if a Doppler-shifted frequency should be higher or lower?+

Use the physical rule as a sanity check before trusting algebra: an approaching source always produces a higher observed frequency, and a receding source always produces a lower one.

Get the Full Wave Behaviour Revision Notes

Complete derivations for Snell's law, standing wave boundary conditions, and the Doppler effect Full worked examples with every trap explained step-by-step All formula, definition, and mistake tables from the IB DP Physics syllabus in one place Practice questions with full worked solutions for Paper 1, 2 and 3 style problems

Get the Wave Behaviour notes on RevisionPrep →

Fields: The IB DP Physics Guide to Flux, Induction & Charged Particle Motion Physics: Nuclear and Quantum Physics (SL)Physics: Nuclear and Quantum Physics (HL)Physics: The Particulate Nature of Matter