IGCSE Physics: Waves, Light, Sound and the Electromagnetic Spectrum

TL;DR

Waves transfer energy without transferring matter, and they can be transverse (like light) or longitudinal (like sound). Light and sound have distinct properties and applications, while the electromagnetic spectrum is a family of transverse waves with varying wavelengths and frequencies. Understanding these wave types helps explain phenomena from radio communication to medical imaging.

1. The Mental Model

Imagine waves as messengers carrying energy across a distance, like a ripple in a pond carrying energy from where you dropped a stone outwards. They don't move the water itself to a new location, just the disturbance. Different types of waves carry different kinds of messages in different ways.

2. The Core Material

What is a Wave?

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A wave is a disturbance that transfers energy through a medium (or even through a vacuum, in the case of electromagnetic waves) without transferring matter.

We have two main types of waves:

• Transverse Waves: The oscillations (vibrations) are perpendicular to the direction of energy transfer.
  • Examples: Light, all electromagnetic waves (radio, microwaves, infrared, visible, UV, X-rays, gamma rays), waves on a string.
  • They have crests (highest points) and troughs (lowest points).
• Longitudinal Waves: The oscillations are parallel to the direction of energy transfer.
  • Examples: Sound waves, waves in a spring (slinky) when pushed and pulled.
  • They have compressions (regions where particles are close together) and rarefactions (regions where particles are spread apart).

Key Wave Properties

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All waves can be described by:

• Wavelength (λ): The distance between two consecutive crests or troughs (for transverse), or two consecutive compressions or rarefactions (for longitudinal). Measured in meters (m).
• Frequency (f): The number of complete waves passing a point per second. Measured in Hertz (Hz).
• Amplitude (A): The maximum displacement of a point from its rest position. For transverse, it's half the height from crest to trough. For longitudinal, it relates to the density changes. It indicates the energy carried by the wave – bigger amplitude means more energy.
• Wave Speed (v): How fast the wave travels. Measured in meters per second (m/s).

The relationship between these is the wave equation:
v = fλ (Speed = Frequency × Wavelength)

Light Waves

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Light is a transverse electromagnetic wave. It can travel through a vacuum and doesn't need a medium. Its speed in a vacuum is approximately $3 \times 10^8$ m/s.

• Reflection: Light bouncing off a surface. Angle of incidence = Angle of reflection.
• Refraction: Light bending as it passes from one medium to another (e.g., air to water) due to a change in speed.
  • When light enters a denser medium (e.g., air to glass), it bends towards the normal.
  • When light enters a less dense medium (e.g., glass to air), it bends away from the normal.
  • This is why lenses work and create images.
• Dispersion: White light splitting into its component colours (ROYGBIV) when refracted, e.g., by a prism, because different colours travel at slightly different speeds in the medium.

Sound Waves

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Sound is a longitudinal mechanical wave. It needs a medium (solid, liquid, or gas) to travel; it cannot travel through a vacuum.

• Speed: Sound travels fastest in solids, slower in liquids, and slowest in gases. This is because particles are closer together in solids, allowing vibrations to transfer more quickly.
• Loudness: Related to the amplitude of the sound wave. Larger amplitude means louder sound.
• Pitch: Related to the frequency of the sound wave. Higher frequency means higher pitch.
• Echoes: Reflections of sound waves.

The Electromagnetic (EM) Spectrum

This is a family of transverse waves, all travelling at the speed of light in a vacuum ($3 \times 10^8$ m/s). They differ only in their wavelength and frequency, which in turn determines their energy and properties.

Here's the EM spectrum from longest wavelength/lowest frequency/lowest energy to shortest wavelength/highest frequency/highest energy:

graph TD
    A["Radio Waves (longest λ)"] --> B["Microwaves"]
    B --> C["Infrared"]
    C --> D["Visible Light"]
    D --> E["Ultraviolet"]
    E --> F["X-rays"]
    F --> G["Gamma Rays (shortest λ, highest f)"]

Each part of the spectrum has specific uses and potential hazards:

• Radio Waves: Communication (TV, radio, mobile phones). Longest wavelength.
• Microwaves: Heating food (microwave ovens), radar, satellite communication.
• Infrared: Remote controls, night vision, thermal imaging, optical fibres. Emitted by hot objects.
• Visible Light: What we see! Photography, illumination, optical fibres.
• Ultraviolet (UV): Sunbeds, sterilisation, detecting forged banknotes. Can cause skin damage.
• X-rays: Medical imaging (broken bones), airport security. Can cause cell mutation.
• Gamma Rays: Sterilising medical equipment and food, cancer treatment (radiotherapy). Highest energy, most ionising.

3. Worked Example

Let's say a sound wave has a frequency of 500 Hz and a wavelength of 0.68 meters. We want to find its speed.

Using the wave equation:
v = fλ

Given:
f = 500 Hz
λ = 0.68 m

Substitute the values:
v = 500 Hz × 0.68 m
v = 340 m/s

So, the speed of this sound wave is 340 meters per second. This is typical for sound in air at room temperature.

Now, let's consider a light wave. All EM waves travel at $3 \times 10^8$ m/s in a vacuum. If a particular colour of visible light has a frequency of $5 \times 10^{14}$ Hz, what is its wavelength?

Using the wave equation rearranged for wavelength:
λ = v / f

Given:
v = 3 \times 10^8 m/s (speed of light in vacuum)
f = 5 \times 10^{14} Hz

Substitute the values:
λ = (3 \times 10^8 m/s) / (5 \times 10^{14} Hz)
λ = 0.6 \times 10^{-6} m
λ = 600 \times 10^{-9} m (or 600 nanometers, nm)

This wavelength falls within the visible light spectrum.

4. Key Takeaways

• Waves transfer energy, not matter, and can be either transverse (oscillations perpendicular) or longitudinal (oscillations parallel).
• The wave equation v = fλ links wave speed, frequency, and wavelength for all waves.
• Light is a transverse electromagnetic wave that can travel through a vacuum, with properties like reflection and refraction.
• Sound is a longitudinal mechanical wave that requires a medium and travels fastest in solids.
• The electromagnetic spectrum is a continuous range of transverse waves (radio to gamma) that all travel at the speed of light in a vacuum but differ in wavelength and frequency.
• Higher frequency/shorter wavelength EM waves (like X-rays and gamma rays) carry more energy and are more hazardous.

Common Mistakes to Avoid:
- Mixing up transverse and longitudinal wave definitions or examples.
- Forgetting that sound needs a medium to travel, while light does not.
- Confusing the effects of amplitude (loudness/intensity) and frequency (pitch/colour) for sound and light.
- Assuming all waves travel at the same speed; only EM waves travel at the same speed in a vacuum.
- Forgetting the order of the EM spectrum and the general trend of energy/wavelength/frequency.

5. Now Try It

Imagine you are designing a communication system. You need to choose between using radio waves and sound waves to send a message across a long distance.

What to do:
1. List three key differences between radio waves and sound waves that would influence your choice for long-distance communication.
2. Based on these differences, explain which type of wave would be more suitable for sending a message across space (where there's a vacuum) and why.
3. Calculate the frequency of a radio wave that has a wavelength of 100 meters, assuming it travels at the speed of light in a vacuum ($3 \times 10^8$ m/s).

What success looks like:
You'll have clearly outlined the properties of both wave types, applied them to a practical scenario, and correctly used the wave equation to solve a problem.