Wave properties: transverse and longitudinal mechanical waves (QCE Physics Unit 2)

What this dot point is asking

QCAA wants you to identify whether a wave is transverse or longitudinal, and to define the five quantities that describe any periodic wave: wavelength, period, frequency, amplitude and speed.

Mechanical waves transfer energy, not matter

A wave is a disturbance that transfers energy through a medium without net transport of the medium itself. Particles oscillate about a fixed position; the disturbance moves through them.

Transverse and longitudinal waves

Transverse waves. Particle motion is perpendicular to the direction of energy propagation. Examples: a wave on a rope or string, surface water waves (approximately), all electromagnetic waves. The wave has crests and troughs.

Longitudinal waves. Particle motion is parallel to the direction of energy propagation. Examples: sound waves in air or water, the primary (P) waves in earthquakes, ultrasound. The wave has compressions (high pressure) and rarefactions (low pressure).

The five quantities

Wavelength ($\lambda$)

Distance between two consecutive points in phase (crest to crest, compression to compression). SI unit: m.

Period ($T$)

Time for one complete cycle to pass a point. SI unit: s.

Frequency ($f$)

Number of cycles per second. $f = 1/T$. SI unit: hertz (Hz).

Amplitude ($A$)

Maximum displacement from equilibrium. SI unit: m for transverse, Pa for sound (pressure amplitude). Amplitude determines wave energy (energy $\propto A^2$).

Speed ($v$)

Distance the wave moves per unit time. $v = f \lambda$. SI unit: m s$^{-1}$. Speed is set by the medium (tension and linear density for strings; bulk modulus and density for sound in fluids; permittivity and permeability for EM).

What changes when a wave crosses media

Frequency stays the same (set by the source). Speed changes (set by the medium). Wavelength adjusts to satisfy $v = f \lambda$.

Examples in context

Example 1. A Bremer River bridge accelerometer logs a $1.8 \text{ Hz}$ transverse vibration of the bridge deck after heavy-truck traffic. Period is $T = 1/f = 0.56 \text{ s}$, wavelength along the $50 \text{ m}$ span (with wave speed $90 \text{ m s}^{-1}$ in the steel structure) is $\lambda = v/f = 50 \text{ m}$, suggesting a first-mode resonance with the span. QCAA EA Unit 2 thematic items pair structural-vibration datasets with the dot-point definitions.

Example 2. A Cairns hospital ultrasound at $5 \text{ MHz}$ uses longitudinal pressure waves (sound) in soft tissue ($v \approx 1540 \text{ m s}^{-1}$), giving $\lambda = 0.31 \text{ mm}$. Compare to a $1.5 \text{ Hz}$ transverse swell on Townsville's Strand at $\lambda = 25 \text{ m}$ (speed $\approx 37 \text{ m s}^{-1}$). Both are mechanical waves, but only the sound is longitudinal. QCAA EA Unit 2 Paper 1 multiple choice typically asks for this transverse-longitudinal identification.

Try this

Q1. Distinguish transverse from longitudinal mechanical waves with one example each. [2 marks]

• Cue. Transverse: particle motion perpendicular to wave propagation (water surface); longitudinal: parallel (sound).

Q2. A wave on a string has wavelength $0.40 \text{ m}$ and frequency $5.0 \text{ Hz}$. Calculate the speed, the period and the amplitude if the maximum displacement is $0.05 \text{ m}$. [3 marks]

• Cue. $v = 2.0 \text{ m s}^{-1}$; $T = 0.20 \text{ s}$; $A = 0.05 \text{ m}$.

Q3. A Bremer River bridge accelerometer detects a $1.8 \text{ Hz}$ transverse deck vibration. (a) Calculate the period. (b) Given a deck wave speed of $90 \text{ m s}^{-1}$, determine the wavelength and discuss whether the $50 \text{ m}$ span supports a first-mode resonance. (c) Distinguish this vibration from longitudinal P-waves used in seismology. [2+3+2 marks; ISMG: Analysis and interpretation, Evaluation]

• Cue. (a) $T = 0.56 \text{ s}$; (b) $\lambda = 50 \text{ m}$, equal to span so first-mode resonance likely; (c) transverse, perpendicular displacement vs longitudinal compressional P-waves.