# Wave Properties

> What waves are, the two main types, and how to measure wavelength, frequency, amplitude and speed.

From HSC Physics on WhizzNotes, free study notes for NSW students: https://whizznotes.com/physics/wave-properties/. Updated 2 November 2026.
Year 11 and Year 12 boxes go deeper than the Year 10 text around them.

### Story time: The stadium wave
At the cricket, the crowd in Bay 12 stood up and threw their arms in the air. Then Bay 13 did it. Then Bay 14. A "Mexican wave" rolled all the way around the stadium in about 30 seconds.

Jack, sitting in Bay 20, noticed something. When the wave reached him, he stood up and sat down. But he never left his seat. Nobody did. The **people** only moved up and down. What travelled around the stadium was the **wave**.

That is exactly how waves in physics work.

**In short:** A wave carries energy from one place to another without carrying matter. Every wave has a wavelength, frequency, amplitude and speed, linked by $v = f\lambda$. Transverse waves (like light) vibrate across the direction of travel, and longitudinal waves (like sound) vibrate along it.

## What is a wave?

A **wave** is a way of **transferring energy** from one place to another **without transferring matter**.

The particles of the material (the **medium**) only **vibrate** back and forth around where they started. The energy moves on.

- Sound waves carry energy from a speaker to your ear. The air does not blow into your ear.
- Ocean waves carry energy to the beach. A floating ball just bobs up and down.

## Two types of waves

**Transverse waves**: the particles vibrate **at right angles** (perpendicular) to the direction the wave travels.
- Examples: waves on a string, ripples on water, light and all electromagnetic waves.
- They have **crests** (high points) and **troughs** (low points).

**Longitudinal waves**: the particles vibrate **parallel** to (along) the direction the wave travels.
- Examples: sound waves, a slinky pushed and pulled from one end.
- They have **compressions** (particles squeezed together) and **rarefactions** (particles spread apart).

### Key idea: The slinky test
Lay a slinky on a table. Flick one end **sideways**: a transverse wave. Push and pull one end **forwards and back**: a longitudinal wave.

## Describing a wave

*Diagram: Transverse wave diagram showing crest, trough, amplitude measured from the middle line to a crest, and wavelength measured from crest to crest*
*Wavelength is crest to crest. Amplitude is the rest position to a crest.*

| Property | Symbol | Meaning | Unit |
|---|---|---|---|
| **Wavelength** | $\lambda$ (lambda) | Length of one complete wave, e.g. crest to crest | metre (m) |
| **Amplitude** | $A$ | Height from the rest position to a crest (or trough). Bigger amplitude = more energy | metre (m) |
| **Frequency** | $f$ | Number of complete waves passing a point each second | hertz (Hz) |
| **Period** | $T$ | Time for one complete wave | second (s) |
| **Wave speed** | $v$ | How fast the wave travels | m/s |

### Watch out: Amplitude is not crest to trough
Amplitude is measured from the **middle** (rest position) to a crest. Crest to trough is **twice** the amplitude.

## The wave equation

$$v = f \lambda$$

Speed = frequency × wavelength. And frequency and period are linked:

$$f = \frac{1}{T} \qquad T = \frac{1}{f}$$

### Worked example: A wave in the pool
Ripples in a pool have a wavelength of 0.5 m. Four ripples pass a point every second.

$$v = f\lambda = 4 \times 0.5 = 2 \text{ m/s}$$

Period: $T = \dfrac{1}{4} = 0.25$ s.

### Key idea: Same medium, same speed
For a given medium, wave speed stays the same. So if frequency goes **up**, wavelength must go **down**. High notes on a piano have short wavelengths. Low notes have long wavelengths.

## Sound waves

Sound is a **longitudinal** wave and needs a **medium** (solid, liquid or gas). It **cannot travel through a vacuum**. In space, nobody can hear you shout.

- Speed of sound in air: about **340 m/s**. Faster in water (about 1500 m/s) and faster still in steel (about 5000 m/s).
- Higher **frequency** = higher **pitch**.
- Bigger **amplitude** = **louder**.
- Humans hear from about **20 Hz to 20 000 Hz**. Above that is **ultrasound**.

**Mind map**

```text
Waves
  Basics
    Transfer energy
    Not matter
    Medium vibrates
  Types
    Transverse: at right angles
    Longitudinal: parallel
    Crests and troughs
    Compressions and rarefactions
  Properties
    Wavelength λ
    Amplitude A
    Frequency f in Hz
    Period T = 1/f
  Equation
    v = fλ
  Sound
    Longitudinal
    Needs a medium
    Pitch = frequency
    Loudness = amplitude
```

### Year 11: Superposition and standing waves
When two waves meet, their displacements **add**. This is **superposition**.

- Crest meets crest: **constructive interference**, a bigger wave.
- Crest meets trough: **destructive interference**, they cancel. Noise cancelling headphones use this.

A wave reflecting back on itself can form a **standing wave** with fixed **nodes** (no movement) and **antinodes** (maximum movement). On a string fixed at both ends:

$$\lambda_n = \frac{2L}{n} \qquad f_n = \frac{nv}{2L}$$

This is how guitar strings and organ pipes make their notes.

### Year 12: The Doppler effect
When a source of waves moves towards you, the waves bunch up and you hear a higher frequency. Moving away, a lower frequency. That is why an ambulance siren drops in pitch as it passes.

$$f' = f\,\frac{v_{\text{wave}} + v_{\text{observer}}}{v_{\text{wave}} - v_{\text{source}}}$$

(using signs for motion towards each other). The same effect with light, called **red shift**, shows that distant galaxies are moving away from us, which is key evidence that the universe is expanding.

## Quick summary

- Waves transfer **energy** without transferring **matter**.
- **Transverse**: vibrations at right angles to travel (light, water ripples).
- **Longitudinal**: vibrations along the direction of travel (sound).
- Wavelength $\lambda$, amplitude $A$, frequency $f$ (Hz), period $T$ (s).
- $v = f\lambda$ and $f = \dfrac{1}{T}$.
- Sound needs a medium. Pitch depends on frequency. Loudness depends on amplitude.

## Quiz

Try these questions from the chapter quiz.

1. Waves transfer:
   - A. Matter only
   - B. Energy without transferring matter
   - C. Both matter and energy equally
   - D. Neither matter nor energy
   - Answer: B. Energy without transferring matter. The medium vibrates in place while energy moves on.

2. Sound waves are:
   - A. Transverse
   - B. Longitudinal
   - C. Electromagnetic
   - D. Unable to travel through solids
   - Answer: B. Longitudinal. Air particles vibrate back and forth in the direction the sound travels.

3. Light waves are:
   - A. Transverse
   - B. Longitudinal
   - C. Sound waves
   - D. Unable to travel through a vacuum
   - Answer: A. Transverse. Light is an electromagnetic wave, which is transverse.

The whole chapter quiz is on the page, for signed-in students: https://whizznotes.com/physics/wave-properties/#quiz