Know that for a longitudinal wave, the direction of vibration is parallel to the direction of propagation and understand that sound waves and seismic P-waves (primary) can be modelled as longitudinal

Published by Patrick Mutisya · 14 days ago

Cambridge IGCSE Physics 0625 – 3.1 General Properties of Waves

3.1 General Properties of Waves

Objective

Know that for a longitudinal wave the direction of vibration is parallel to the direction of propagation and understand that sound waves and seismic P‑waves (primary waves) can be modelled as longitudinal.

Key Concepts

  • A wave transports energy without the permanent displacement of matter.

  • Two fundamental types of mechanical waves:

    • Transverse waves – particle displacement is perpendicular to the direction of travel.

    • Longitudinal waves – particle displacement is parallel to the direction of travel.

  • In a longitudinal wave the medium experiences alternating compressions (regions of higher pressure) and rarefactions (regions of lower pressure).

Longitudinal Wave Illustration

Suggested diagram: A series of springs or slinky showing compressions and rarefactions moving to the right, with arrows indicating particle motion parallel to the wave direction.

Mathematical Description

The speed \$v\$ of a wave is related to its frequency \$f\$ and wavelength \$\lambda\$ by

\$v = f \lambda\$

For longitudinal waves in a gas, the speed of sound can be expressed as

\$v = \sqrt{\frac{\gamma\,R\,T}{M}}\$

where \$\gamma\$ is the adiabatic index, \$R\$ the universal gas constant, \$T\$ the absolute temperature, and \$M\$ the molar mass of the gas.

Comparison of Wave Types

PropertyTransverse WaveLongitudinal Wave
Particle displacementPerpendicular to propagationParallel to propagation
Typical examplesLight, water surface waves, string vibrationsSound in air, seismic P‑waves, compression waves in springs
Regions of disturbanceCrests and troughsCompressions and rarefactions
Medium requirementCan travel in solids, liquids, or gases (e.g., light is electromagnetic)Requires a material medium (solid, liquid, or gas)

Sound Waves as Longitudinal Waves

When a source vibrates (e.g., a speaker diaphragm), it pushes adjacent air molecules together, creating a compression. The molecules then move apart, forming a rarefaction. This alternating pattern travels outward, while individual air molecules oscillate back and forth along the same line as the wave travels.

Seismic P‑Waves (Primary Waves)

P‑waves are the fastest seismic waves generated by earthquakes. They propagate through the Earth’s interior by compressing and expanding the material in the direction of travel, exactly as a longitudinal wave does. Because they can move through solids, liquids, and gases, P‑waves are the first to be recorded by seismographs.

Summary Checklist

  1. Identify the direction of particle vibration relative to wave propagation.

  2. Recognise compressions and rarefactions as the characteristic features of longitudinal waves.

  3. Apply the wave speed formula \$v = f\lambda\$ to longitudinal waves.

  4. Explain why sound in air and seismic P‑waves are modelled as longitudinal waves.