A wave is a disturbance that propagates through a material medium (or, for electromagnetic waves, through empty space) and carries energy from one location to another **without transporting matter permanently**.
2. Key terminology (Cambridge IGCSE 0625)
Term
Definition
Wave‑front
A line (in 2‑D) or surface (in 3‑D) joining points that are in the same phase of motion (e.g. all crests at a given instant).
Wavelength λ
Distance between two successive points that are in phase – most commonly between two consecutive crests or two consecutive compressions.
Frequency f
Number of complete cycles that pass a given point each second (unit Hz).
Period T
Time for one complete cycle; T = 1/f.
Amplitude A
Maximum displacement of particles from their equilibrium position. Energy carried by a wave is proportional to the square of the amplitude (E ∝ A²).
Crest / Trough
Highest (crest) and lowest (trough) points of a transverse wave.
Compression / Rarefaction
Regions of higher and lower particle density in a longitudinal wave.
Wave speed v
Rate at which the wave‑front moves through the medium (m s⁻¹).
3. Energy transfer without matter transfer
Particles of the medium undergo a temporary displacement and then return to their original positions.
The net displacement of any particle over one complete cycle is zero, so there is **no permanent transport of matter** – only energy is conveyed.
Because the energy carried is proportional to A², a larger amplitude means a more energetic wave, even though the particles travel the same short distance back and forth.
4. Particle motion – transverse vs. longitudinal
Transverse wave – particle motion is **perpendicular** (⊥) to the direction of wave propagation. Examples: water‑surface waves, electromagnetic waves. See Fig. 1: a sketch showing crests, troughs and arrows indicating up‑and‑down motion.
Longitudinal wave – particle motion is **parallel** (∥) to the direction of wave propagation. Examples: sound in air, seismic P‑waves. See Fig. 2: a sketch showing a series of compressions and rarefactions with arrows pointing forward and backward.
5. Wave‑speed relationship
The fundamental wave equation links speed, frequency and wavelength:
$$v = f\,\lambda$$
where v is in m s⁻¹, f in Hz and λ in m.
Worked example
Question: A tuning‑fork vibrates at 500 Hz and produces a sound wave in air with a wavelength of 0.68 m. Find the speed of the sound wave.
Solution:
Write the wave equation: v = f λ.
Substitute the given values: v = 500 Hz × 0.68 m.
Calculate: v = 340 m s⁻¹.
Result: The sound travels at 340 m s⁻¹ in the given conditions – a typical speed for sound in air at room temperature.
6. Types of waves
Property
Mechanical waves
Electromagnetic waves
Medium required
Yes – solid, liquid or gas
No – can travel in vacuum
Particle motion
Transverse, longitudinal or both
Transverse only (oscillating electric & magnetic fields)
Typical speeds
~300 m s⁻¹ (sound in air) to several km s⁻¹ (seismic S‑waves)
≈ 3.00 × 10⁸ m s⁻¹ (speed of light)
Examples
Sound, water‑surface waves, seismic S‑waves
Light, radio, microwaves, X‑rays
7. Wave behaviours
Reflection – when a wave meets a barrier and returns into the medium it came from. Law of reflection:* Angle of incidence = angle of reflection (θᵢ = θʳ).
Refraction – change in direction when a wave passes from one medium to another where its speed is different. Snell’s law (for light):* \( \displaystyle \frac{\sin\theta_1}{\sin\theta_2}= \frac{v_1}{v_2}= \frac{n_2}{n_1}\) where n is the refractive index.
Diffraction – bending of waves around an obstacle or through an opening whose size is comparable to the wavelength. Diffraction condition:* Significant diffraction occurs when the size of the aperture or obstacle ≲ λ.
Ripple‑tank demonstration (Fig. 3): A shallow tray of water produces circular ripples. The ripples illustrate:
Reflection at a barrier,
Refraction when they pass into a region of different depth (speed changes),
Diffraction through a narrow slit.
8. Common misconceptions
“Waves carry matter.” – Particles only oscillate about an equilibrium position; there is no net transport of matter.
“All waves need a medium.” – Electromagnetic waves propagate through empty space.
“Higher frequency always means a faster wave.” – Speed depends on the medium; frequency and wavelength adjust to keep v = fλ.
“Only transverse waves have crests and troughs.” – Crests and troughs describe the shape of any wave‑front; longitudinal waves are described by compressions and rarefactions.
9. Summary
Waves transfer energy while the medium’s particles undergo temporary, reversible displacements.
Key features: wave‑front, wavelength, frequency, period, amplitude (E ∝ A²), crest, trough, compression, rarefaction, and speed.
Fundamental relationship: v = fλ – be able to rearrange for any of the three variables.
Mechanical waves need a material medium; electromagnetic waves do not.
Particle motion distinguishes transverse (⊥) from longitudinal (∥) waves.
Reflection, refraction (Snell’s law) and diffraction (λ‑size condition) are characteristic behaviours observable in ripple‑tank experiments and everyday life.
Fig. 1 – Transverse wave: crests, troughs and particle motion ⟂ to the direction of travel.Fig. 2 – Longitudinal wave: compressions, rarefactions and particle motion ∥ to the direction of travel.Fig. 3 – Ripple‑tank showing reflection, refraction (depth change) and diffraction (slit).
Your generous donation helps us continue providing free Cambridge IGCSE & A-Level resources,
past papers, syllabus notes, revision questions, and high-quality online tutoring to students across Kenya.