Wave characteristics

IB Physics SL· Topic 3: Wave behaviour, 3.2 Wave characteristics· 18 min read

1. Types of Waves★☆☆☆☆⏱ 4 min

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Waves transfer energy from one point to another without transferring matter. They are classified based on the direction of particle oscillation relative to the direction of energy propagation.

📘 Definition

Transverse Wave

A wave where particles of the medium oscillate perpendicular to the direction of energy transfer

Example:

Electromagnetic waves, waves on a stretched string, seismic S-waves

📘 Definition

Longitudinal Wave

A wave where particles of the medium oscillate parallel to the direction of energy transfer

Example:

Sound waves, seismic P-waves, pressure waves in a slinky

📐 Worked Example

Classify each of the following as transverse or longitudinal: (a) X-rays, (b) ultrasound from a medical scanner, (c) ripples on a water surface.

1
Recall the two definitions: transverse = oscillation perpendicular to energy flow, longitudinal = oscillation parallel to energy flow.
2
Analyze (a): X-rays are a form of electromagnetic radiation, so they are transverse.
3
Analyze (b): Ultrasound is a high-frequency sound wave, so it is longitudinal.
4
Analyze (c): Water surface ripples have particles moving in circles, but the net oscillation is perpendicular to the direction of travel, so they are transverse.

Exam tip:

Always refer to the direction of oscillation relative to energy transfer, not any other frame of reference when classifying waves.

2. Graphs and Key Wave Parameters★★☆☆☆⏱ 5 min

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Two common graphs are used to represent wave motion, and it is critical to distinguish what information each provides.

Graph Type	X-Axis	Extractable Parameters	Non-Extractable Parameters
Displacement-Time	Time $t$	Amplitude $A$ , Period $T$	Wavelength $λ$
Displacement-Distance	Position $x$	Amplitude $A$ , Wavelength $λ$	Period $T$

Core key definitions for wave parameters are:

📘 Definition

Frequency

$f$

Number of full cycles per second, $f = \frac{1}{T}$ , measured in Hertz (Hz)

📘 Definition

Wavelength

$λ$

Shortest distance between two points on a wave that are in phase, measured in meters (m)

📐 Worked Example

A displacement-time graph for a wave shows one full cycle takes 0.02 s. The wave speed is 340 m/s. Calculate the wavelength of the wave.

1
Extract period from the displacement-time graph: $T = 0.02$ s.
2
Calculate frequency from period:
3
$f = \frac{1}{T} = \frac{1}{0.02} = 50 \text{ Hz}$
4
Rearrange the wave equation to solve for wavelength:
5
$\lambda = \frac{v}{f} = \frac{340}{50} = 6.8 \text{ m}$

3. Wave Equation and Phase Difference★★☆☆☆⏱ 5 min

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All travelling waves follow the fundamental wave equation that relates wave speed, frequency and wavelength. Wave speed is the speed at which energy propagates through the medium.

v = f \lambda

📘 Definition

Phase Difference

$Δ ϕ$

The difference in oscillation phase between two points on a wave, measured in radians. One full wavelength separation gives a phase difference of $2 π$ radians.

For two points separated by distance $Δ x$ , phase difference is calculated as:

\Delta \phi = 2\pi \frac{\Delta x}{\lambda}

📐 Worked Example

Two points on a wave are 0.25 m apart. The wavelength of the wave is 1.0 m. What is the phase difference between the two points?

1
Substitute the values into the phase difference formula:
2
$\Delta \phi = 2\pi \times \frac{0.25}{1.0} = 0.5\pi = \frac{\pi}{2} \text{ radians}$
3
This means the two points are one quarter of a cycle out of phase with each other.

✓ Quick check

Test your understanding:

What is the phase difference between two points 2 wavelengths apart?
- $2 π$ radians
- $4 π$ radians
- $π$ radians
- $2$ radians
Reveal answer
$4\pi$ radians —
One wavelength = $2 π$ radians, so two wavelengths = $2 \times 2 π = 4 π$ radians.

4. Wave Intensity★★★☆☆⏱ 4 min

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Intensity measures the rate of energy transfer per unit area by a wave. It is a commonly tested relationship between intensity and amplitude.

📘 Definition

Intensity

$I$

Power transferred per unit area perpendicular to the wave direction, measured in $W m^{- 2}$

Intensity is proportional to the square of the wave amplitude: $I \propto A^{2}$ . For a point source emitting waves equally in all directions, intensity also follows the inverse square law with distance from the source: $I \propto \frac{1}{r ^{2}}$ , where $r$ is distance from the source.

📐 Worked Example

At a distance of 2 m from a point source, the amplitude of a sound wave is 0.1 m. What is the amplitude at a distance of 4 m from the source?

1
Combine the two proportionalities: $I \propto \frac{A ^{2}}{r ^{2}}$ . Intensity is proportional to $A^{2}$ and inversely proportional to $r^{2}$ , so:
2
$\frac{A_1^2}{r_1^2} = \frac{A_2^2}{r_2^2} \implies \frac{A_1}{r_1} = \frac{A_2}{r_2}$
3
Rearrange to solve for the new amplitude $A_{2}$ :
4
$A_2 = A_1 \times \frac{r_1}{r_2} = 0.1 \times \frac{2}{4} = 0.05 \text{ m}$

5. Common Pitfalls

Wrong move:

Extracting wavelength directly from a displacement-time graph

Why:

Displacement-time graphs plot against time, not distance, so wavelength cannot be read directly

Correct move:

Use the graph to get period, calculate frequency, then use $v = f λ$ to find wavelength

Wrong move:

Rearranging the wave equation as $λ = \frac{f}{v}$

Why:

Common algebraic error that loses easy marks in exams

Correct move:

Remember $v = f \times λ$ , so $λ = \frac{v}{f}$

Wrong move:

Claiming intensity is proportional to amplitude

Why:

The relationship is non-linear, and this is a common multiple-choice trap

Correct move:

Memorize $I \propto A^{2}$ , intensity scales with the square of amplitude

Wrong move:

Confusing transverse and longitudinal sound waves

Why:

Many students mix up sound with electromagnetic waves

Correct move:

All sound waves in gases/liquids are longitudinal, only electromagnetic waves are transverse

Wrong move:

Stating one wavelength corresponds to $π$ radians phase difference

Why:

Confusing full cycle phase difference with half cycle

Correct move:

One full wavelength (one full cycle) = $2 π$ radians, half wavelength = $π$ radians

6. Quick Reference Cheatsheet

Parameter	Symbol	Key Relationship	Units
Amplitude	$A$	Max displacement from equilibrium	m
Wavelength	$λ$	Distance between in-phase points	m
Period	$T$	$T = 1/ f$	s
Frequency	$f$	$f = 1/ T$	Hz
Wave speed	$v$	$v = f λ$	m/s
Phase difference	$Δ ϕ$	$Δ ϕ = 2 π (Δ x / λ)$	radians
Intensity	$I$	$I \propto A^{2}$ , $I \propto 1/ r^{2}$	W/m²
Transverse wave		Oscillation ⊥ energy direction
Longitudinal wave		Oscillation ∥ energy direction

7. Frequently Asked

What is the difference between the two common wave graphs?

Displacement-time graphs plot particle displacement against time, so you can get period and amplitude, but not wavelength. Displacement-distance graphs plot displacement against position along the wave, so you get wavelength and amplitude, but not period.

Do all waves follow $v = f λ$ ?

All progressive (travelling) waves obey this relationship, regardless of whether they are mechanical or electromagnetic.

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2025 · Paper 1
Wave intensity amplitude ratio
2024 · Paper 2
Compare transverse/longitudinal waves
2023 · Paper 1
Phase difference calculation

What's Next

Wave characteristics form the foundation for all further topics in wave behaviour for IB Physics SL. All wave phenomena including refraction, reflection, interference, diffraction and standing waves build on these core definitions and relationships. This sub-topic is regularly tested in both Paper 1 (multiple choice) and Paper 2 (structured questions) so mastering these concepts will give you a strong base for more complex wave problems. You will next apply these characteristics to specific wave behaviours and interactions.