Wave Parameters

A-Level Physics· Unit 7: Waves· 30 min read

1. Core Wave Parameter Definitions★☆☆☆☆⏱ 10 min

The following core parameters are routinely tested in definition questions in both Paper 1 and Paper 2 of CIE 9702. You must be able to recall and write each definition exactly to earn full marks.

Parameter	Definition	SI Unit
Displacement	Distance + direction from equilibrium	m
Amplitude	Maximum displacement from equilibrium	m
Wavelength	Distance between consecutive in-phase points	m
Period	Time for one full oscillation	s
Frequency	Number of oscillations per second	Hz (s⁻¹)
Wave speed	Distance travelled per unit time	m s⁻¹

📐 Worked Example

A wave completes 20 full oscillations in 5.0 seconds. State the period and frequency of the wave.

1
Period T is time per oscillation, so divide total time by number of oscillations:
2
$T = \frac{5.0}{20} = 0.25 \text{ s}$
3
Frequency is the reciprocal of period:
4
$f = \frac{1}{T} = \frac{1}{0.25} = 4.0 \text{ Hz}$

Exam tip:

Always mention equilibrium for displacement/amplitude and 'consecutive' for wavelength to get full marks for definitions.

2. The Universal Wave Equation★★☆☆☆⏱ 15 min

All waves (mechanical and electromagnetic) obey the fundamental wave equation, derived directly from the definitions of wave speed, period and frequency.

🔬 Derivation

Goal:

Derive the wave equation $v = f λ$

Starting from:

In one period $T$ , a wave travels exactly one wavelength $λ$

1
Speed equals distance divided by time:
2
$v = \frac{\lambda}{T}$
3
Substitute $f = \frac{1}{T}$ :
4
$v = \lambda \times f = f\lambda$

Result:

This equation applies to all waves, regardless of type.

📐 Worked Example

Calculate the speed of red light with wavelength 700 nm and frequency $4.3 \times 1 0^{14}$ Hz in a vacuum.

1
Convert wavelength to SI units (metres):
2
$700 \text{ nm} = 700 \times 10^{-9} = 7.0 \times 10^{-7} \text{ m}$
3
Substitute into $v = f λ$ :
4
$v = (4.3 \times 10^{14}) \times (7.0 \times 10^{-7}) = 3.01 \times 10^8 \text{ m s}^{-1}$

Exam tip:

Always convert all quantities to SI units before substitution to avoid order of magnitude errors.

3. Phase and Phase Difference★★☆☆☆⏱ 15 min

Phase describes the position of an oscillation in its cycle, while phase difference measures how far out of step two oscillations are.

📘 Definition

Phase Difference

The difference in phase between two points on a wave, measuring how much one oscillation is ahead or behind another.

Example:

Two points one wavelength apart have a phase difference of $2 π$ radians (360°) and are in phase.

\text{Phase difference } \Delta\phi = \frac{\Delta x}{\lambda} \times 2\pi \text{ (radians)}

📐 Worked Example

Two points on a wave of wavelength 1.2 m are separated by 0.3 m. Calculate the phase difference in radians.

1
Use the phase difference formula:
2
$\Delta\phi = \frac{\Delta x}{\lambda} \times 2\pi$
3
Substitute values:
4
$\Delta\phi = \frac{0.3}{1.2} \times 2\pi = \frac{\pi}{2} \text{ radians}$

Exam tip:

Always check if the question asks for radians or degrees, and give your answer in the required unit.

4. Graphical Representations of Waves★★★☆☆⏱ 15 min

There are two standard graphs used to represent waves, each showing different core parameters. Examiners regularly test the distinction between these two graph types.

Graph Type	Axes	Parameters Read Directly
Displacement-Position	y: Displacement, x: Position along wave	Amplitude, Wavelength
Displacement-Time	y: Displacement, x: Time of oscillation	Amplitude, Period

📐 Worked Example

A displacement-time graph shows one full oscillation from $t = 0$ to $t = 0.1$ s, with maximum displacement 2.0 cm. Find amplitude and frequency.

1
Amplitude is maximum displacement, read directly from the graph:
2
$A = 2.0 \text{ cm} = 0.020 \text{ m}$
3
Period is time for one full oscillation: $T = 0.1$ s
4
Calculate frequency as reciprocal of period:
5
$f = \frac{1}{T} = \frac{1}{0.1} = 10 \text{ Hz}$

Exam tip:

Remember: period comes from time graphs, wavelength comes from position graphs.

5. Common Pitfalls

Wrong move:

Defining wavelength as 'distance between two points in phase' without 'consecutive'

Why:

Points multiple wavelengths apart are also in phase, so the definition is incomplete

Correct move:

Always include 'consecutive' in your wavelength definition to earn full marks

Wrong move:

Trying to read period from a displacement-position graph, or wavelength from a displacement-time graph

Why:

Position graphs show the wave at one instant, so they contain no time period information

Correct move:

Stick to the rule: period from time graphs, wavelength from position graphs

Wrong move:

Using non-SI units like nanometres or centimetres directly in the wave equation

Why:

This leads to incorrect orders of magnitude, even if the method is correct

Correct move:

Always convert all units to metres and seconds before substituting into calculations

Wrong move:

Leaving phase difference in degrees when the question asks for radians

Why:

Examiners do not award marks for answers in the wrong unit, even if the value is correct

Correct move:

Double-check the required unit for phase difference at the end of your calculation

6. Quick Reference Cheatsheet

Quantity	Relationship	SI Unit
Frequency $f$	$f = 1/ T$	Hz
Period $T$	$T = 1/ f$	s
Wave speed	$v = f λ$	m s⁻¹
Phase difference	$Δ ϕ = (Δ x / λ) \times 2 π$	radians
Displacement-position graph	Reads $A$ , $λ$	n/a
Displacement-time graph	Reads $A$ , $T$	n/a

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.

2022 · 12
Phase difference calculation
2023 · 21
Wave parameter definitions
2021 · 13
Wave equation application

What's Next

Wave parameters are the foundation for all subsequent wave topics in CIE A-Level Physics, including transverse/longitudinal waves, interference, diffraction, standing waves and the electromagnetic spectrum. A strong mastery of these definitions and relationships will make every more complex wave topic much easier to understand, as most exam questions require you to apply these core concepts to new scenarios. Common extended response questions combine wave parameter calculations with wave phenomena like superposition and double-slit interference. Next, you will build on this knowledge to explore the properties of different wave types.