Know that waves transfer energy without transferring matter

3.1 General Properties of Waves

1. What is a wave?

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)

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:

1. Write the wave equation: v = f λ.
2. Substitute the given values: v = 500 Hz × 0.68 m.
3. 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

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):* \( \displaystyle \frac{\sin\theta1}{\sin\theta2}= \frac{v1}{v2}= \frac{n2}{n1}\) 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

1. “Waves carry matter.” – Particles only oscillate about an equilibrium position; there is no net transport of matter.
2. “All waves need a medium.” – Electromagnetic waves propagate through empty space.
3. “Higher frequency always means a faster wave.” – Speed depends on the medium; frequency and wavelength adjust to keep v = fλ.
4. “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.