# General Properties of Waves

> Physics · CIE IGCSE 0625
> Source: https://www.owlsprep.com/study/cie-0625-u3-general-properties-of-waves/

This guide covers all Core and Extended content for CIE IGCSE Physics 0625 Unit 3.1 General Properties of Waves, including wave types, key calculations, and exam-tested wave behaviours.

**Prerequisites:** [Physical quantities and unit conversion](https://www.owlsprep.com/study/cie-0625-u1-physical-quantities-units/); [Basic graph interpretation skills](https://www.owlsprep.com/study/cie-0625-u1-graph-interpretation/)

## Learning objectives

- Define waves and distinguish between transverse and longitudinal wave types
- Recall and apply the wave equation $v = f\lambda$ for calculations
- Describe the core wave behaviours: reflection, refraction, and diffraction
- Interpret displacement-time and displacement-distance wave graphs (Extended only)
- Explain changes to wave speed, frequency and wavelength during refraction (Extended only)

## Wave Types (Core)

**Wave** — A disturbance that transfers energy from one point to another without transferring matter. Particles of the medium only vibrate around a fixed position.

*Example:* Ripples on a pond transfer energy across the water surface, but individual water molecules do not travel with the ripple.

There are two main categories of waves, distinguished by the direction of particle vibration relative to energy transfer:

- **Transverse waves**: Vibrations are perpendicular (90°) to the direction of energy transfer. Examples include light, water ripples, and seismic S-waves.
- **Longitudinal waves**: Vibrations are parallel to the direction of energy transfer. They form regions of compression (high density) and rarefaction (low density) in the medium. Examples include sound and seismic P-waves.

**Worked example:** Classify each of the following waves as transverse or longitudinal: (a) X-rays, (b) sound waves in steel, (c) waves on a stretched string, (d) ultrasound waves

1. Step 1: Recall that electromagnetic waves (including X-rays) and mechanical waves on strings are always transverse.
2. Step 2: Recall that all sound waves (including ultrasound) are longitudinal, regardless of the medium they travel through.
3. Final answer: (a) Transverse, (b) Longitudinal, (c) Transverse, (d) Longitudinal

> **Exam tip:** When asked to distinguish between wave types, always mention both the direction of vibration and the direction of energy transfer to get full marks.

## Key Wave Quantities & Wave Equation (Core + Extended)

All waves share 4 core measurable quantities, defined below:

- **Amplitude (A)**: Maximum displacement of a particle from its rest position, measured in metres (m). Higher amplitude = higher energy (e.g. louder sound, brighter light).
- **Wavelength (λ)**: Distance between two consecutive identical points on adjacent waves (e.g. peak to peak, compression to compression), measured in metres (m).
- **Frequency (f)**: Number of complete waves passing a fixed point per second, measured in hertz (Hz). 1 Hz = 1 wave per second.
- **Period (T)**: Time taken for one complete wave to pass a fixed point, measured in seconds (s). $f = \frac{1}{T}$ and $T = \frac{1}{f}$.

**Wave Equation** — Relates wave speed (v, m/s), frequency (f, Hz) and wavelength (λ, m). Wave speed is determined by the medium the wave travels through.

*Notation:* v = f\lambda

**Worked example:** A radio wave has a frequency of 90.9 MHz. Calculate its wavelength, given that the speed of electromagnetic waves in air is $3 \times 10^8$ m/s.

1. Step 1: Convert frequency to SI units: 90.9 MHz = $90.9 \times 10^6$ Hz = $9.09 \times 10^7$ Hz.
2. $$\lambda = \frac{v}{f} = \frac{3 \times 10^8}{9.09 \times 10^7} \approx 3.3 m$$
3. Final answer: 3.3 m (2 significant figures)

> **Exam tip:** Always convert all values to SI units before substituting into the wave equation: convert cm to m, kHz/MHz to Hz, etc.

*Calculator:* allowed

## Core Wave Behaviours

All waves exhibit 3 key behaviours, tested regularly in exams:

- **Reflection**: Waves bounce off a barrier. The angle of incidence equals the angle of reflection. Frequency, speed, and wavelength stay constant; only direction changes.
- **Refraction**: Waves enter a new medium at an angle. Speed and wavelength change; frequency stays constant; direction changes if speed changes.
- **Diffraction**: Waves spread out when passing through a gap or around an obstacle. Frequency, speed, and wavelength all stay constant.

> **Exam tip:** For reflection, refraction and diffraction, remember frequency always stays constant; only refraction (a change of medium) also changes the wave speed and wavelength.

## Extended: Wave Graphs & Refraction Calculations

Extended candidates need to interpret two types of wave graphs:

- **Displacement-distance graph**: Shows displacement of particles against distance from the wave source. Amplitude = maximum displacement on the y-axis; Wavelength = distance between two consecutive peaks on the x-axis.
- **Displacement-time graph**: Shows displacement of a single particle against time. Amplitude = maximum displacement on the y-axis; Period = time between two consecutive peaks on the x-axis; Frequency = 1/period.

**Worked example:** A light wave travels from air (speed $3 \times 10^8$ m/s, wavelength 500 nm) into water, where its speed drops to $2.25 \times 10^8$ m/s. Calculate the wavelength of the light in water.

1. Step 1: Recall that frequency is constant when a wave changes medium, so $f = \frac{v_1}{\lambda_1} = \frac{v_2}{\lambda_2}$.
2. $$\lambda_2 = \frac{v_2 \times \lambda_1}{v_1} = \frac{2.25 \times 10^8 \times 500}{3 \times 10^8} = 375 nm$$
3. Final answer: 375 nm

*Calculator:* allowed

## Extended: Diffraction, Wavelength and Gap Size

Extended candidates must describe how the amount of diffraction depends on the wavelength of the wave compared with the size of the gap or obstacle:

- **Diffraction through a gap**: The waves spread out more as the gap becomes narrower. Maximum diffraction occurs when the gap size is approximately equal to the wavelength of the wave. If the gap is much wider than the wavelength, the waves pass almost straight through, with only slight spreading at the edges.
- **Diffraction at an edge**: Waves also spread out as they pass the edge of an obstacle. For a given obstacle, longer wavelengths diffract (spread) more than shorter wavelengths.

**Worked example:** Explain why AM radio waves (wavelength ~100 m) can be received in valleys where FM radio waves (wavelength ~3 m) cannot.

1. Step 1: Recall that longer wavelengths diffract more than shorter wavelengths.
2. Step 2: AM radio waves have a much longer wavelength than FM waves, so they diffract around hills and into valleys. FM waves are too short to diffract significantly, so they are blocked by hills.

> **Exam tip:** For diffraction questions, always link the gap size or obstacle size to the wavelength of the wave to get full marks.

## Common pitfalls

- **Wrong:** Confusing vibration directions for transverse and longitudinal waves
  - Why it fails: Students often mix up parallel vs perpendicular to energy transfer
  - Correct: Use the mnemonic: **T**ransverse = Perpendicular (both have 'e' as the second letter), **L**ongitudinal = Parallel (both start with 'l')
- **Wrong:** Using peak-to-trough distance as amplitude
  - Why it fails: Amplitude is the maximum displacement from rest position, not total distance between peak and trough
  - Correct: Divide peak-to-trough distance by 2 to get the correct amplitude value
- **Wrong:** Assuming frequency changes during refraction
  - Why it fails: Students see speed and wavelength change, so incorrectly assume frequency also changes
  - Correct: Frequency is determined only by the wave source, so it stays constant for all wave behaviours
- **Wrong:** Forgetting unit conversion in wave equation calculations
  - Why it fails: Wavelength is often given in cm or nm, while speed is given in m/s, leading to incorrect results
  - Correct: Always convert all quantities to SI units (m, s, Hz) before substituting into the formula
- **Wrong:** Stating that diffraction changes wave speed or wavelength
  - Why it fails: Students associate direction change with speed change, as seen in refraction
  - Correct: Diffraction does not change the medium, so speed, wavelength, and frequency all remain constant

## Cheatsheet

| Quantity | Symbol | SI Unit | Tier | Key Information |
| --- | --- | --- | --- | --- |
| Amplitude | A | m | Core | Max displacement from rest; linked to wave energy |
| Wavelength | λ | m | Core | Distance between consecutive identical wave points |
| Frequency | f | Hz | Core | Waves per second; $f=1/T$; constant for all wave behaviours |
| Wave speed | v | m/s | Core | $v=fλ$; determined only by the medium |
| Reflection | - | - | Core | Angle i = angle r; v, f, λ all constant |
| Refraction | - | - | Core | v and λ change; f constant; direction changes if incident at angle |
| Diffraction | - | - | Core | Waves spread through a gap or around an obstacle; v, f, λ all constant |
| Diffraction (gap-size effect) | - | - | Extended | Max diffraction when gap size ≈ λ; longer wavelengths diffract more |
| Wave graphs | - | - | Extended | Displacement-distance gives λ; displacement-time gives T |

## What's next

Now that you have mastered the general properties of waves, you are ready to explore specific wave types tested in CIE IGCSE Physics 0625. Next, you will study the electromagnetic spectrum, a family of transverse waves with wide real-world applications, followed by sound waves, the most common example of longitudinal waves. You will also learn to draw wave diagrams for reflection, refraction and diffraction, and practice structured exam questions to consolidate your knowledge and maximize your marks.

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