Wave properties (wavelength, frequency, amplitude, period, wave speed $v = f\lambda$), transverse vs longitudinal waves, sound waves, the wave behaviours (reflection, refraction, diffraction, interference, polarisation), the Doppler effect, and the electromagnetic spectrum

What this dot point is asking

QCAA wants Year 11 students to describe wave properties, distinguish wave types, apply $v = f\lambda$, and identify wave behaviours.

Wave properties

**Wavelength $\lambda$** (m): distance between successive crests / troughs.

**Frequency $f$** (Hz = 1/s): waves per second.

**Period $T = 1/f$** (s): time for one wavelength to pass.

Amplitude: maximum displacement from equilibrium. Determines energy.

**Wave speed $v = f\lambda$**.

Transverse vs longitudinal

Transverse. Oscillation perpendicular to propagation direction. Examples: light, water surface, transverse waves on a string.

Longitudinal. Oscillation parallel to propagation. Compressions and rarefactions. Examples: sound, P waves in earthquakes.

Only transverse waves can be polarised.

Sound waves

Longitudinal mechanical wave. Speed in air at 20 degrees C: $\sim 343$ m/s. Speed depends on medium (faster in solids than liquids than gases). Requires a medium; cannot travel through vacuum.

Audible range: 20 Hz to 20 kHz (human, declines with age). Below 20 Hz: infrasound. Above 20 kHz: ultrasound.

Intensity in W/m$^2$. Loudness in decibels (logarithmic).

Wave behaviours

Reflection. Wave bounces off boundary. Angle of incidence = angle of reflection.

Refraction. Wave changes direction at boundary between media (different speeds).

Diffraction. Wave bends around obstacles or through openings. Greater when wavelength comparable to opening.

Interference. Two waves superpose: constructive (in phase) and destructive (out of phase).

Polarisation. Only transverse waves. Light passing through polariser: $I = I_0 \cos^2 \theta$ (Malus's law).

Doppler effect

Apparent frequency change when source and observer move relative to each other.

If source moves toward observer, perceived frequency increases. If away, decreases.

$f_{\text{observed}} = f_{\text{source}} (v / (v - v_s))$ for source moving toward observer at speed $v_s$, with wave speed $v$.

Applications: radar speed measurement, medical ultrasound, astronomy (red/blueshift).

Electromagnetic spectrum

All EM waves: transverse, travel at $c = 3 \times 10^8$ m/s in vacuum. Differ in wavelength / frequency.

Photon energy $E = hf$. Higher frequency = higher energy.

Common errors

Confusing wave types. Light is transverse; sound is longitudinal.

Forgetting medium for sound. Sound requires a medium; cannot travel through vacuum.

Mixing $v$ and $c$. Light in vacuum: $c$. Light in medium: $c/n$ where $n$ is refractive index.

Doppler direction. Approaching: higher frequency. Receding: lower.

In one sentence

Waves transfer energy without net matter movement; properties are wavelength, frequency, period, amplitude, and wave speed $v = f\lambda$; transverse waves (light) oscillate perpendicular to propagation, longitudinal waves (sound) oscillate parallel; wave behaviours (reflection, refraction, diffraction, interference, polarisation), the Doppler effect, and the electromagnetic spectrum (radio to gamma, all at $c$ in vacuum) are the universal wave phenomena.