Wave Properties

This lesson covers the fundamental properties of waves — the two main types, key terminology, and the wave equation — as required by the Edexcel GCSE Physics specification (1PH0), Topic 4: Waves. You need to understand how waves transfer energy, distinguish between transverse and longitudinal waves, and use the wave equation confidently in calculations.

What Is a Wave?

A wave is a disturbance that transfers energy from one place to another without transferring matter. The particles of the medium vibrate about their rest position — they do not travel along with the wave.

Key facts about waves:

Waves transfer energy and information from one place to another.
Waves do not transfer matter — the medium itself does not move from source to destination.
Waves can travel through a medium (e.g. sound through air) or through a vacuum (e.g. light, electromagnetic waves).
Examples of waves: water waves, sound waves, light waves, seismic waves, electromagnetic waves.

Exam Tip: A very common exam question asks "What do waves transfer?" The answer is always energy (and information). Never say that waves transfer matter — this is a key misconception the examiners test.

Types of Waves

There are two main types of wave: transverse waves and longitudinal waves. The difference is the direction in which the particles of the medium oscillate relative to the direction of energy transfer.

Transverse Waves

In a transverse wave, the oscillations (vibrations) of the particles are perpendicular (at right angles) to the direction of energy transfer.

Examples of transverse waves:

Light and all electromagnetic waves
Water waves (on the surface)
Waves on a string or rope
S-waves (secondary seismic waves)

In a transverse wave, you can identify peaks (crests) and troughs — the highest and lowest points of the wave.

Longitudinal Waves

In a longitudinal wave, the oscillations of the particles are parallel to the direction of energy transfer. The particles vibrate back and forth along the same direction the wave travels.

Examples of longitudinal waves:

Sound waves
P-waves (primary seismic waves)
Ultrasound waves
Waves in a slinky spring (when pushed and pulled along its length)

In a longitudinal wave, you can identify regions of compression (where particles are pushed close together) and rarefaction (where particles are spread further apart).

Exam Tip: To remember the difference — Transverse = oscillations are aT right angles to direction of travel. Longitudinal = oscillations are aLong the direction of travel.

Key Wave Terminology

You must know the following terms and be able to identify them on wave diagrams:

Term	Definition	Unit
Amplitude (A)	The maximum displacement of a point on the wave from its rest (equilibrium) position	metres (m)
Wavelength (λ)	The distance between two consecutive points in phase (e.g. crest to crest, or trough to trough)	metres (m)
Frequency (f)	The number of complete waves passing a point per second	hertz (Hz)
Period (T)	The time taken for one complete wave to pass a point	seconds (s)
Wave speed (v)	The speed at which the wave moves through the medium	metres per second (m/s)

Important Relationships

Wavelength can be measured from any point on one wave to the same point on the next wave — crest to crest, trough to trough, or any identical point.
Amplitude is measured from the rest position to the crest (or trough), not from crest to trough. The distance from crest to trough is twice the amplitude.
Frequency and period are inversely related:

T = 1 / f and f = 1 / T

Exam Tip: A very common mistake is to measure amplitude as the distance from peak to trough. This gives you double the amplitude. Always measure from the rest position (the middle line) to the peak.

Transverse Wave Diagram

graph LR
    A["Peak (crest)"] -.-> B["← Wavelength (λ) →"]
    B -.-> C["Peak (crest)"]
    D["Rest position"] -.-> E["↑ Amplitude (A)"]
    D -.-> F["↓ Amplitude (A)"]
    F -.-> G["Trough"]

    style A fill:#2980b9,color:#fff
    style C fill:#2980b9,color:#fff
    style G fill:#c0392b,color:#fff
    style D fill:#27ae60,color:#fff

On a transverse wave diagram:

The wavelength is the horizontal distance from one crest to the next crest (or one trough to the next trough).
The amplitude is the vertical distance from the rest position to the crest (or from the rest position to the trough).
The rest position is the horizontal line through the middle of the wave.

Longitudinal Wave Diagram

In a longitudinal wave diagram:

Compressions are regions where particles are close together (high pressure).
Rarefactions are regions where particles are spread apart (low pressure).
The wavelength is the distance from one compression to the next compression (or one rarefaction to the next rarefaction).

graph LR
    A["Compression<br/>(particles close)"] --> B["Rarefaction<br/>(particles spread)"]
    B --> C["Compression<br/>(particles close)"]
    C --> D["Rarefaction<br/>(particles spread)"]

    style A fill:#e74c3c,color:#fff
    style B fill:#3498db,color:#fff
    style C fill:#e74c3c,color:#fff
    style D fill:#3498db,color:#fff

The Wave Equation

The wave equation links wave speed, frequency, and wavelength:

v = f × λ

Where:

v = wave speed (m/s)
f = frequency (Hz)
λ = wavelength (m)

This equation is on the Edexcel Physics equation sheet.

Rearranging the Wave Equation

To find frequency: f = v / λ
To find wavelength: λ = v / f

Worked Examples

Example 1: Finding Wave Speed

A wave has a frequency of 5 Hz and a wavelength of 2 m. Calculate the wave speed.

v = f × λ

v = 5 × 2

v = 10 m/s

Example 2: Finding Wavelength

A radio wave travels at 3 × 10⁸ m/s and has a frequency of 100 MHz (100 × 10⁶ Hz). Calculate the wavelength.

λ = v / f

λ = (3 × 10⁸) / (100 × 10⁶)

λ = (3 × 10⁸) / (1 × 10⁸)

λ = 3 m

Example 3: Finding Frequency from Period

A wave has a period of 0.02 s. Calculate its frequency.

f = 1 / T

f = 1 / 0.02

f = 50 Hz

Example 4: Combined Calculation

A wave has a period of 0.005 s and a wavelength of 1.5 m. Calculate the wave speed.

Step 1: Find the frequency.

f = 1 / T = 1 / 0.005 = 200 Hz

Step 2: Use the wave equation.

v = f × λ = 200 × 1.5

v = 300 m/s

Exam Tip: Always show your working clearly, including rearranging the equation. Write the formula first, then substitute the values, then calculate the answer with the correct unit. If the period is given instead of frequency, convert it first using f = 1/T.

Summary

Waves transfer energy without transferring matter.
Transverse waves: oscillations are perpendicular to the direction of energy transfer (e.g. light, water waves, EM waves, S-waves).
Longitudinal waves: oscillations are parallel to the direction of energy transfer (e.g. sound, P-waves).
Key terms: amplitude (maximum displacement from rest), wavelength (distance for one complete wave), frequency (number of waves per second), period (time for one wave).
The wave equation: v = f × λ.
Period and frequency are related by: T = 1 / f.
Amplitude is measured from the rest position — not from crest to trough.