Describe the longitudinal nature of sound waves

Published by Patrick Mutisya · 14 days ago

Cambridge IGCSE Physics 0625 – 3.4 Sound: Longitudinal Nature of Sound Waves

3.4 Sound – Longitudinal Nature of Sound Waves

What is a Longitudinal Wave?

A longitudinal wave is a disturbance in which the particles of the medium vibrate parallel to the direction of wave propagation. In other words, the particle motion is along the same line as the energy travel.

How Sound Waves Propagate

Sound in gases, liquids and solids travels as a longitudinal wave. When a source (e.g., a vibrating tuning‑fork) moves forward it compresses the nearby particles, creating a region of higher pressure called a compression. As the source moves back, it leaves a region of lower pressure known as a rarefaction. These alternating compressions and rarefactions travel through the medium.

Suggested diagram: A series of particles showing alternating compressions and rarefactions with arrows indicating particle motion parallel to the direction of wave travel.

Key Features of Longitudinal Sound Waves

  • Particle displacement is parallel to the direction of wave travel.

  • Energy is transmitted through successive compressions and rarefactions.

  • The wave can travel through any material that can be compressed (gases, liquids, solids).

  • The speed of sound depends on the medium’s elasticity and density, given by \$v = \sqrt{\frac{B}{\rho}}\$ where \$B\$ is the bulk modulus and \$\rho\$ is the density.

Comparison with Transverse Waves

PropertyLongitudinal Wave (Sound)Transverse Wave (e.g., Light, Wave on a String)
Particle MotionParallel to direction of propagationPerpendicular to direction of propagation
Typical MediaGases, liquids, solids (must be compressible)Solids (string), electromagnetic fields (vacuum)
Wave ElementsCompressions and rarefactionsCrests and troughs
Speed DependenceDepends on bulk modulus and densityDepends on tension and linear density (string) or is constant \$c\$ in vacuum (light)

Mathematical Description of a Simple Harmonic Sound Wave

The displacement \$s\$ of a particle in a sinusoidal sound wave can be expressed as:

\$s(x,t) = s_{\max}\,\sin\!\bigl(kx - \omega t\bigr)\$

where:

  • \$s_{\max}\$ – amplitude of particle displacement

  • \$k = \dfrac{2\pi}{\lambda}\$ – wave number

  • \$\omega = 2\pi f\$ – angular frequency

  • \$\lambda\$ – wavelength

  • \$f\$ – frequency

Why Sound is Perceived as a Longitudinal Wave

  1. The ear detects changes in pressure caused by compressions and rarefactions.

  2. These pressure variations cause the eardrum to vibrate back and forth, mirroring the longitudinal particle motion.

  3. The brain interprets the vibration frequency as pitch and the amplitude as loudness.

Common Misconceptions

  • “Sound travels like a ripple on water.” – Water ripples are surface transverse waves; sound in water is longitudinal.

  • “The air itself moves from the source to the listener.” – Air particles oscillate about fixed positions; only the pressure disturbance travels.

Summary

Sound waves are longitudinal because the particles of the medium vibrate in the same direction that the wave travels. This results in alternating regions of compression and rarefaction that propagate the acoustic energy through gases, liquids and solids. Understanding the longitudinal nature of sound is essential for analysing wave speed, frequency, pitch, and the interaction of sound with different media.