Waves - Sciences - Co-ordinated (Double) (0654) - Cambridge IGCSE

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P3 Waves: Comprehensive Study Notes for IGCSE Co-ordinated Sciences (0654)

Hello future scientists! This chapter, 'Waves', is fundamental to understanding how energy moves all around us—from the light that lets you read these notes to the sound of your favourite music. Don't worry if some concepts seem a little abstract; we'll break down how waves work using simple ideas and real-world examples!

P3.1 General Properties of Waves

The most important idea about waves is what they do and what they don't do:

What waves transfer: Energy.
What waves do not transfer: Matter (the medium).

Think of a stadium crowd doing "The Wave". The energy (the movement) travels around the stadium, but the people (the matter/medium) stay in their seats!

Key Definitions of Wave Features

When we look at a wave, there are specific characteristics we need to define:

Crest (Peak): The highest point of a wave.
Trough: The lowest point of a wave.
Amplitude (A): The maximum displacement of a point from the rest (equilibrium) position. It relates to the energy or intensity of the wave. (e.g., louder sound means higher amplitude).
Wavelength ($\lambda$): The distance between two consecutive corresponding points (e.g., crest to crest or trough to trough).
Frequency (f): The number of complete waves passing a point per second. Measured in Hertz (Hz).
Wave Speed (v): The speed at which the energy moves through the medium.

Quick Review: The Universal Wave Equation (Core Content)
The speed of any wave is related to its frequency and wavelength:

$$v = f\lambda$$

Where:

$v$ = wave speed (m/s)
$f$ = frequency (Hz)
$\lambda$ = wavelength (m)

Memory Trick: Velocity = Frequency × Lambda!

P3.1.6 Types of Waves (Core & Supplement)

We classify waves based on the direction the particles of the medium vibrate relative to the direction the energy travels (propagation).

1. Transverse Waves (Supplement)

In a Transverse Wave, the vibrations are at right angles ($90^\circ$) (perpendicular) to the direction the wave is travelling.

Examples: Electromagnetic (EM) waves (like light and radio), water waves, and seismic S-waves (secondary).

Analogy: Shaking a rope up and down. The rope moves vertically (vibration), but the energy moves horizontally (propagation).

2. Longitudinal Waves (Supplement)

In a Longitudinal Wave, the vibrations are parallel to the direction the wave is travelling.

Examples: Sound waves and seismic P-waves (primary).
These waves consist of alternating regions of high and low pressure:
- Compressions: Regions where the particles are crowded together (high pressure).
- Rarefactions: Regions where the particles are spread apart (low pressure).

Analogy: Pushing and pulling a Slinky (spring) forwards and backwards.

KEY TAKEAWAY P3.1: Waves move energy, not matter. Transverse waves vibrate perpendicular to motion (light). Longitudinal waves vibrate parallel to motion (sound).

P3.1 & P3.2 Wave Behaviours: Reflection, Refraction, and Diffraction

Waves interact with boundaries and obstacles in predictable ways.

1. Reflection (Core)

Reflection is when a wave bounces off a surface.

The Law of Reflection (P3.2.1 Core): The angle of incidence ($i$) is equal to the angle of reflection ($r$). (i.e., $i = r$).
We measure these angles from the Normal, which is a dashed line drawn perpendicular to the surface at the point where the ray hits.

Image Formation by a Plane Mirror (P3.2.1 Core & Supplement)

A simple flat mirror (plane mirror) produces an image that is:

Same size as the object.
Same distance behind the mirror as the object is in front.
Laterally inverted (left/right reversed—like seeing your reflection).
Virtual (Supplement): The image is formed where the light rays appear to come from, but the rays do not actually pass through that point. You cannot project a virtual image onto a screen.

Common mistake: Students often forget to draw the Normal when measuring angles of incidence and reflection!

2. Refraction (Core)

Refraction is the change in direction of a wave (like light) as it passes from one medium to another (e.g., from air to water).

What causes refraction? A change in the speed of the wave.

When light travels from a less dense medium (like air) to a more dense medium (like glass), it slows down and bends towards the normal.
When light travels from a more dense medium to a less dense medium, it speeds up and bends away from the normal.

Refractive Index (n) (Supplement)

The refractive index, $n$, measures how much a material slows down light.

$$n = \frac{\sin i}{\sin r}$$

Where:

$i$ = angle of incidence
$r$ = angle of refraction

3. Total Internal Reflection (TIR) (Supplement)

This is a special type of reflection that happens when light tries to move from a more dense medium (like glass) to a less dense medium (like air).

Step-by-step TIR:

Light travels from dense medium (Glass/Water) towards less dense medium (Air).
As the angle of incidence ($i$) increases, the angle of refraction ($r$) also increases (it bends away from the normal).
At a specific angle, the angle of refraction reaches $90^\circ$. This angle of incidence is called the Critical Angle ($c$).
If the angle of incidence is greater than the critical angle ($i > c$), the light ray does not leave the dense medium but is reflected fully back inside. This is Total Internal Reflection.

Application: Optical fibres use TIR to transmit data (like internet signals) or images (in medicine) over long distances, bouncing the light repeatedly inside the fibre core.

4. Diffraction (Supplement)

Diffraction is the spreading of waves as they pass through a narrow gap or around the edge of an obstacle.

Key Factor: Diffraction is most noticeable (maximum spreading) when the size of the gap is approximately equal to the wavelength ($\lambda$) of the wave.
If the gap is much wider than the wavelength, little diffraction occurs.

KEY TAKEAWAY P3.2: Reflection means bouncing back ($i=r$). Refraction means bending due to speed change. TIR is total reflection inside a dense medium when $i > c$.

P3.2.4 Dispersion of Light (Core)

When white light enters a transparent medium, like a glass prism, it separates into its component colours. This is called dispersion.

This happens because each colour of light has a slightly different wavelength and therefore travels at a slightly different speed through the glass, causing different amounts of refraction.
The colours separate into the Visible Spectrum: Red, Orange, Yellow, Green, Blue, Indigo, Violet (ROYGBIV).

Order Check:

Red is refracted the least (longest wavelength, lowest frequency).
Violet is refracted the most (shortest wavelength, highest frequency).

P3.3 Electromagnetic Spectrum

The Electromagnetic (EM) Spectrum is a family of transverse waves that all travel at the same incredibly high speed in a vacuum.

Crucial Fact: All EM waves travel at the speed of light in a vacuum, which is $3.0 \times 10^8 \text{ m/s}$ (Supplement). This speed is approximately the same in air.

Regions in Order of Increasing Frequency (and Decreasing Wavelength) (Core)

The order is crucial for the exam. Here is the spectrum, moving from lowest frequency/longest wavelength to highest frequency/shortest wavelength:

Radio waves
Microwaves
Infrared (IR)
Visible Light
Ultraviolet (UV)
X-rays
Gamma rays

Mnemonic: Really Many Instruments Visit Us X-tra Greatly (Radio, Microwave, IR, Visible, UV, X-ray, Gamma).

Applications and Harmful Effects (Core)

Did you know? The only EM wave region we can see is visible light, which makes up only a tiny fraction of the whole spectrum!

QUICK REVIEW EM SPECTRUM: All regions travel at $3 \times 10^8 \text{ m/s}$. The order (Radio to Gamma) is the order of increasing frequency and increasing danger.

P3.4 Sound Waves

Sound is a mechanical wave, meaning it requires a medium (matter) to travel through. It is an example of a longitudinal wave.

Properties of Sound (Core & Supplement)

Production: Sound is produced by vibrating sources (e.g., vocal cords, guitar strings, speakers).
Nature (Supplement): Sound waves in air are longitudinal, consisting of alternating compressions (high pressure) and rarefactions (low pressure).
Audible Range: The human ear can typically hear frequencies between 20 Hz and 20 kHz.
Speed (Core & Supplement): Sound generally travels fastest in solids, slower in liquids, and slowest in gases.
- Air speed is roughly 330–340 m/s, much slower than light.

Measuring Speed of Sound (Core)

To determine the speed of sound in air, you need to measure a distance ($S$) and the time ($t$) it takes for the sound to travel that distance (often over a long distance using an echo or two microphones).

$$v = \frac{S}{t}$$

Loudness and Pitch (Core)

When you listen to sound, the characteristics you hear relate directly to the wave properties:

Loudness: Controlled by the Amplitude. Higher amplitude means louder sound.
Pitch: Controlled by the Frequency. Higher frequency means higher pitch.

Echoes and Ultrasound (Core)

Echo: An echo is simply the reflection of a sound wave off a surface (like a wall or cliff face).
Ultrasound: Sound waves with a frequency higher than 20 kHz (beyond human hearing). Used widely in medical imaging and industrial scanning.

KEY TAKEAWAY P3.4: Sound is a longitudinal wave created by vibration. It needs a medium. Loudness is amplitude; pitch is frequency. Speed ranking: Solid > Liquid > Gas.