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 $v = f \lambda$.

Worked example

A musician plays middle C, which has a frequency of $262$ Hz, in air where the speed of sound is $343$ m s$^{-1}$. Find the wavelength.

$\lambda = v / f = 343 / 262 = 1.31$ m.

If the same note enters water (where the speed of sound is approximately $1480$ m s$^{-1}$), the frequency stays at $262$ Hz, so $\lambda_{\text{water}} = 1480 / 262 = 5.65$ m.

Common traps

Confusing amplitude with wavelength. Amplitude is the height of a crest (perpendicular to motion for transverse). Wavelength is the horizontal distance between repeats.

Treating speed as a property of the wave. Wave speed is a property of the medium, not the source. A whistle and a piano playing the same note have the same wavelength in the same air.

Calling sound transverse. Sound is longitudinal in air, water and solids in compression. Solids can also carry transverse sound (S-waves), but the air-borne sound we hear is longitudinal.

Mixing $f$ and $T$ on the calculator. A $2$ Hz wave has a period of $0.5$ s, not $2$ s.

In one sentence

Mechanical waves transfer energy through a medium and are classified as transverse (particle motion perpendicular to wave direction: rope, EM waves) or longitudinal (parallel: sound, P-waves), with each wave described by wavelength $\lambda$, period $T$, frequency $f = 1/T$, amplitude $A$, and speed $v = f \lambda$ set by the medium.