Describe mechanical waves as transverse or longitudinal, identifying their characteristics including wavelength, period, frequency, amplitude and speed, and giving examples of each

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.