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

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

TL;DR

All waves transfer energy without moving matter; they have wavelength, frequency, amplitude and speed linked by v = fλ. Light and sound are waves but behave differently—light is electromagnetic and travels through a vacuum, sound needs a medium and travels slower. The electromagnetic spectrum is a continuous range of waves from radio to gamma rays, all travelling at the speed of light.

1. The Mental Model

Imagine a slinky spring stretched across a table. When you shake one end, a ripple travels along it—but the coils themselves don't march forward; they just bob up and down in place. That bobbing is a wave: it carries energy (the motion) through space without actually moving the spring itself. Light, sound, water ripples—all the same idea. The key difference? Sound needs that spring (or air, or water); light doesn't—it zooms through empty space because it is the disturbance in electric and magnetic fields, not in a physical medium.

2. The Core Material

2.1 What Makes a Wave a Wave?

A wave has four core properties you need to know cold:

• Wavelength (λ): distance between two adjacent peaks (or troughs, or any matching points). Measured in metres.
• Frequency (f): how many complete waves pass a point per second. Measured in hertz (Hz); 1 Hz = 1 wave per second.
• Amplitude (A): height of the wave from the centre line to peak (or trough). Bigger amplitude = more energy being carried.
• Speed (v): how fast the wave travels through its medium. All three are linked by the equation:

$$v = f \lambda$$

This is the relationship for waves. It works for sound, light, water, everything. If frequency goes up and speed stays the same, wavelength must go down—they're inverses of each other.

2.2 Sound Waves

Sound is a longitudinal wave—the particles of the medium (air, water, solid) vibrate back and forth along the direction the sound is travelling. Imagine blowing a whistle: your lips create compressions and rarefactions in the air that march outward.

Key facts about sound:
- Needs a medium to travel (air, water, metal). No medium = no sound. That's why space is silent.
- Speed in air at room temperature: ~330 m/s. Slower than light.
- Speed depends on temperature and the medium. Sound travels faster through solids and liquids than air (roughly 1500 m/s in water, 5000 m/s in steel).
- Frequency you hear ranges from ~20 Hz (subsonic bass) to ~20,000 Hz (ultrasonic squeaks). Humans can't hear outside that range; dogs and bats can.
- Loudness is determined by amplitude. Higher amplitude = louder sound.

2.3 Light Waves

Light is a transverse wave—the electric and magnetic fields oscillate perpendicular to the direction the light travels. It's not a ripple in a physical medium; it is the ripple in the electromagnetic field itself.

Key facts about light:
- Does NOT need a medium. Travels through vacuum at ~3 × 10⁸ m/s (speed of light, c).
- Much faster than sound—that's why you see lightning before hearing thunder.
- Visible light has wavelengths from ~400 nm (violet) to ~700 nm (red). Shorter wavelength = higher frequency = higher energy per photon.
- Colour depends on frequency, not on medium. Red light stays red whether it travels through air, water, or glass—the frequency doesn't change.

2.4 The Electromagnetic Spectrum

The EM spectrum is a continuous range of waves, all made of electric and magnetic fields, all travelling at speed c in vacuum. They're ordered by frequency (or wavelength):

Radio ← Microwave ← Infrared ← Visible ← UV ← X-ray ← Gamma
(low frequency, long wavelength)    →    (high frequency, short wavelength)

Real-world uses:
- Radio: broadcasting, communication
- Microwave: heating food, mobile phones, radar
- Infrared: heat lamps, night vision, thermography
- Visible: the only range your eye detects (~400–700 nm)
- Ultraviolet: tanning (damages skin), sterilising equipment
- X-rays: medical imaging, penetrating soft tissue
- Gamma rays: nuclear decay, cancer treatment, sterilising pharmaceuticals

The spectrum is continuous, not chunked. There's no gap between radio and microwave—one transitions smoothly into the other as frequency increases.

graph LR
    A["Radio<br/>~10⁻¹ m<br/>~10⁶ Hz"] --> B["Microwave<br/>~10⁻³ m<br/>~10⁹ Hz"]
    B --> C["Infrared<br/>~10⁻⁶ m<br/>~10¹² Hz"]
    C --> D["Visible<br/>400–700 nm<br/>~10¹⁵ Hz"]
    D --> E["UV<br/>~10⁻⁸ m<br/>~10¹⁶ Hz"]
    E --> F["X-ray<br/>~10⁻¹⁰ m<br/>~10¹⁸ Hz"]
    F --> G["Gamma<br/>~10⁻¹² m<br/>~10²⁰ Hz"]

    style D fill:#ffff99
    style A fill:#ff9999
    style B fill:#ff9999
    style C fill:#ffcc99
    style E fill:#cc99ff
    style F fill:#99ccff
    style G fill:#99ccff

2.5 Key Differences: Sound vs Light

3. Worked Example

Problem: A radio station broadcasts at a frequency of 98 MHz. Light from that same transmitter travels at 3 × 10⁸ m/s. What is the wavelength of the radio wave?

Solution:
1. Convert frequency to Hz: 98 MHz = 98 × 10⁶ Hz = 9.8 × 10⁷ Hz
2. Use v = fλ, rearranged to λ = v / f
3. λ = (3 × 10⁸ m/s) / (9.8 × 10⁷ Hz)
4. λ = 3.06 m (approximately 3 metres)

Interpretation: Radio waves at this frequency are about 3 metres long. That's why old radio antennas could be that long—they were designed to resonate at the same length as the incoming wavelength, boosting reception. Visible light, by contrast, has a wavelength of a few hundred nanometres (billionths of a metre), which is why you can't see the individual "peaks" of light the way you'd see ripples in a pond.

4. Examiner's Breakdown

4.1 What Examiners Actually Reward

1. State the equation v = fλ and use it correctly, substituting actual numbers with units and showing the rearrangement step—not just plugging values into a calculator.
2. Distinguish between longitudinal and transverse waves explicitly: "Sound is longitudinal because particles vibrate parallel to the direction of travel; light is transverse because the electric and magnetic fields oscillate perpendicular to the direction of travel."
3. Explain why sound cannot travel through a vacuum by referring to the need for a medium to vibrate. Do NOT just say "it can't"; explain why.
4. Order the electromagnetic spectrum correctly from lowest to highest frequency (or longest to shortest wavelength): radio, microwave, infrared, visible, UV, X-ray, gamma.
5. Relate frequency, wavelength and energy: "Shorter wavelength (higher frequency) means higher energy per photon in the electromagnetic spectrum."
6. Use the term 'continuous spectrum' correctly: explain that there are no gaps between different types of EM radiation—one blends smoothly into the next.

4.2 Trapdoor Mistakes

4.3 Score-Boosting Comparisons

5. Now Try It

Task: You're given this data for a sound wave in air:
- Frequency: 440 Hz (middle A on a piano)
- Speed of sound in air: 330 m/s

(a) Calculate the wavelength of this sound wave.
(b) If the same frequency sound wave travelled through water (speed ≈ 1500 m/s), what would its wavelength be? Explain why the wavelength changed but the frequency did not.
(c) Now consider visible light with a frequency of 5 × 10¹⁴ Hz. Calculate its wavelength. Why is this wavelength so much smaller than the sound wave's?

Model answer must include:
- Correct rearrangement of v = fλ to λ = v / f for part (a)
- Numerical answer: ~0.75 m
- Part (b): wavelength ≈ 3.4 m; explanation that frequency is determined by the source, not the medium, but speed depends on the medium, so λ must increase
- Part (c): wavelength ≈ 6 × 10⁻⁷ m (600 nm); statement that light has much higher frequency than sound, so using v = fλ with the same v (3 × 10⁸ m/s) but much larger f, the wavelength must be proportionally smaller

Success looks like: All three calculations are correct with working shown, and you've explained why frequency staysthe same but wavelength and speed change when the medium changes.

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