Science - Combined (0653) | Waves

Study Notes: P3 Waves (IGCSE Combined Science 0653)

Welcome to the exciting world of waves! This chapter is essential for understanding how energy moves through space and matter—it covers everything from the light that allows you to read these notes, to the sound of your favourite music, and even the Wi-Fi that connects your devices.
Don't worry if some concepts seem tricky at first; we will break them down using simple examples and handy tricks!

P3.1 General Properties of Waves

A wave is a disturbance that transfers energy from one place to another without transferring matter. Think of throwing a stone into a pond: the ripples move outwards, but the water itself just moves up and down (oscillates) in the same spot.

Wave Motion and Features (Core Content)

Waves are often illustrated by the vibration (oscillation) of ropes, springs, or water.

• Crest (or Peak): The highest point of the wave.
• Trough: The lowest point of the wave.
• Amplitude (\(A\)): The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium (rest) position. (The bigger the amplitude, the more energy the wave carries!)
• Wavelength (\(\lambda\), lambda): The distance between a point on one wave and the identical point on the next wave (e.g., crest to crest or trough to trough).
• Frequency (\(f\)): The number of waves passing a point every second. Measured in Hertz (Hz).

The Wave Equation (Core Content)

The speed at which a wave travels (\(v\)) depends on its frequency (\(f\)) and its wavelength (\(\lambda\)).

Wave Speed = Frequency × Wavelength

$$v = f\lambda$$

Where:
\(v\) is the wave speed (m/s)
\(f\) is the frequency (Hz)
\(\lambda\) is the wavelength (m)
(Memory Aid: "Velocity is Funky Lambda".)

Types of Waves: Transverse vs. Longitudinal (Supplement Content)

Waves are classified based on how the particles in the medium vibrate compared to the direction the energy travels (propagation).

1. Transverse Waves:
   • The direction of vibration (oscillation) is at right angles (perpendicular) to the direction the wave is travelling (propagation).
   • Examples: All electromagnetic waves (light, radio, X-rays), water waves, and seismic S-waves (secondary).
   • Memory Aid: Imagine doing "The Wave" in a stadium (up and down motion), but the energy moves around the stadium (forwards).
2. Longitudinal Waves:
   • The direction of vibration is parallel to the direction the wave is travelling.
   • They consist of regions of compressions (where particles are squashed together, high pressure) and rarefactions (where particles are spread apart, low pressure).
   • Examples: Sound waves and seismic P-waves (primary).

Wave Interactions (Core Content)

Waves can interact with boundaries in different ways:

1. Reflection: This happens when a wave bounces off a surface (like light reflecting off a mirror or sound reflecting off a wall, creating an echo).
2. Refraction: This is the change in the wave's direction as it passes from one medium to another, caused by a change in speed. (Think of a car hitting mud at an angle—it slows down and changes direction.)

P3.2 Light

Light is a form of electromagnetic radiation and an important transverse wave.

P3.2.1 Reflection of Light

When light hits a plane (flat) surface, it reflects according to specific rules:

1. The Normal is an imaginary line drawn perpendicular (at 90°) to the reflecting surface at the point where the ray hits.
2. The Angle of incidence (\(i\)) is the angle between the incident ray and the Normal.
3. The Angle of reflection (\(r\)) is the angle between the reflected ray and the Normal.

Law of Reflection (Core Content): The angle of incidence is equal to the angle of reflection: \(i = r\).

Images in a Plane Mirror (Core/Supplement):
When you look into a plane mirror, the image you see has specific characteristics:

• It is the same size as the object.
• It is the same distance behind the mirror as the object is in front.
• It is laterally inverted (left and right are swapped, like an ambulance writing).
• It is virtual. This is a key term! A virtual image means that the light rays appear to come from the image, but they don't actually pass through that location. You cannot project a virtual image onto a screen.

P3.2.2 Refraction of Light

Definition (Core Content): Refraction is the change in direction of a light ray passing from one transparent medium to another (e.g., from air to glass), caused by a change in its speed.

What happens at the boundary?

• When light moves from a less dense medium (like air) to a more dense medium (like glass or water), it slows down and bends towards the Normal.
• When light moves from a more dense medium (like glass) to a less dense medium (like air), it speeds up and bends away from the Normal.

P3.2.3 Thin Converging Lens (Core Content)

A converging lens (or convex lens) is thicker in the middle than at the edges. Its purpose is to make parallel rays of light meet (converge) at a single point.

Key Terms for Lenses

• Principal Axis: The line passing horizontally through the centre of the lens.
• Principal Focus (\(F\)) / Focal Point: The point on the principal axis where rays parallel to the axis meet after passing through the lens.
• Focal Length (\(f\)): The distance between the centre of the lens and the principal focus.

Image Characteristics (Real Images Only)

By interpreting ray diagrams, you must be able to describe the image formed by a converging lens (for real images):

• If the image is formed on the opposite side of the lens from the object, it is a real image (light rays actually pass through it).
• Real images are always inverted (upside down).
• The size can be enlarged, diminished (smaller), or the same size, depending on the object's distance from the lens.

P3.2.4 Dispersion of Light (Core Content)

Dispersion is the spreading of white light into its component colours when it passes through a prism (or water droplets, causing a rainbow).

This happens because different colours (wavelengths) of light travel at slightly different speeds in the glass, causing them to be refracted by different amounts.

The visible spectrum is ordered by wavelength and frequency.

• Order of Wavelength (Longest to Shortest): Red, Orange, Yellow, Green, Blue, Indigo, Violet (ROYGBIV)
• Order of Frequency (Lowest to Highest): Red, Orange, Yellow, Green, Blue, Indigo, Violet

P3.3 Electromagnetic Spectrum

The Electromagnetic (EM) Spectrum is a family of transverse waves. They are all fundamentally the same but differ in frequency and wavelength.

General Properties

• Speed (Core/Supplement): All EM waves travel at the same high speed in a vacuum (and approximately the same speed in air). This speed is the speed of light, \(c\).
  $$c = 3.0 \times 10^8 \text{ m/s}$$
• They are transverse waves.
• They do not require a medium to travel (they can travel through a vacuum, like space).

The Order of the Spectrum (Core Content)

You must know the regions in order of increasing frequency (and decreasing wavelength).

$$ \text{Radio Waves} \rightarrow \text{Microwaves} \rightarrow \text{Infrared} \rightarrow \text{Visible Light} \rightarrow \text{Ultraviolet (UV)} \rightarrow \text{X-rays} \rightarrow \text{Gamma Rays} $$

(Memory Aid: Really Many Invisible Visitors Use X-ray Glasses.)

Region	Applications (Uses)	Harmful Effects (Excessive Exposure)
Radio Waves	Radio and television transmissions, radar.	None listed on syllabus.
Microwaves	Satellite television, mobile (cell) phones, microwave ovens.	None listed on syllabus.
Infrared	Remote controllers for televisions, thermal imaging (e.g., night vision).	None listed on syllabus. (Though intense IR can cause burns.)
Visible Light	Vision, photography.	None listed on syllabus.
Ultraviolet (UV)	Detecting fake bank notes.	Damage to surface cells and eyes, leading to skin cancer and eye conditions.
X-rays	Medical scanning, security scanners (e.g., airport).	Mutation or damage to cells in the body (due to high energy).
Gamma Rays	Detection of cancer and its treatment (radiotherapy).

Did you know? The shorter the wavelength (and higher the frequency), the more energy the EM wave carries, which is why X-rays and Gamma rays are the most harmful to living cells.

P3.4 Sound

Sound waves are mechanical waves caused by vibrations that require a medium (solid, liquid, or gas) to travel. They are longitudinal waves.

Production and Characteristics (Core Content)

• Production: Sound is produced by vibrating sources (e.g., a vibrating guitar string, vocal cords).
• Transmission: Sound needs a medium (particles) to transmit the energy. It cannot travel through a vacuum.
• Audible Range: Humans can typically hear sound frequencies between 20 Hz and 20 kHz (20 000 Hz).
• Ultrasound: Sound with a frequency higher than 20 kHz.
• Loudness: Affected by the wave’s amplitude (larger amplitude = louder sound).
• Pitch: Affected by the wave’s frequency (higher frequency = higher pitch).

Sound as a Longitudinal Wave (Supplement Content)

In a gas (like air), a vibrating source causes air particles to oscillate parallel to the wave direction, creating alternating regions:

• Compressions: Regions of higher pressure where particles are crowded together.
• Rarefactions: Regions of lower pressure where particles are spread further apart.

Speed of Sound (Core/Supplement)

The speed of sound depends on the medium it travels through.

General Speed Rule (Supplement): Sound travels fastest in solids, slower in liquids, and slowest in gases.

Why? Because particles are closest together in solids, allowing vibrations (energy) to be passed on most quickly.

Example Speeds (approx.):

• Air: ~330 m/s
• Water: ~1500 m/s
• Steel: ~5000 m/s

Reflection of Sound (Echoes)

An echo is simply the reflection of a sound wave.

Determining the Speed of Sound (Core Content)

The speed of sound in air can be determined by measuring the time (\(t\)) taken for sound to travel a known distance (\(d\)) (often using an echo off a distant wall).

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

If using an echo method, remember that the sound travels to the wall and back, so the total distance travelled is \(2d\).