Waves and sound: QCE Physics Unit 2 Year 11

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.

Examples in context

Example 1. A Brisbane River ferry sounds a $200 \text{ Hz}$ horn at $30 \text{ m s}^{-1}$ approaching South Bank. A listener on the pontoon hears $f' = f \times v/(v - v_s) = 200 \times 340/(340-30) = 219 \text{ Hz}$ - the Doppler effect from the QCAA Unit 2 dot point on sound. The wavelength ahead of the ferry compresses to $\lambda' = (v - v_s)/f = 1.55 \text{ m}$ from the rest-frame $1.70 \text{ m}$.

Example 2. ANSTO Mt Cotton dishes track $2.2 \text{ GHz}$ telemetry from a $7 \text{ km s}^{-1}$ orbital satellite using radial-velocity Doppler. The shift $\Delta f / f \approx v/c = 2.3 \times 10^{-5}$ gives $\Delta f \approx 51 \text{ kHz}$ - tens of thousands of times the audible Doppler, measurable in real time and used to derive orbital parameters. QCAA EA Unit 2 thematic items hook on this electromagnetic-vs-acoustic parallel.

Try this

Q1. State the electromagnetic spectrum in order of increasing frequency. [2 marks]

• Cue. Radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.

Q2. A source emits $440 \text{ Hz}$ and moves toward an observer at $20 \text{ m s}^{-1}$ ($v_{sound} = 340 \text{ m s}^{-1}$). Calculate the observed frequency. [3 marks]

• Cue. $f' = f \times v/(v - v_s) = 440 \times 340/320 = 467.5 \text{ Hz}$.

Q3. A Brisbane River ferry horn at $200 \text{ Hz}$ approaches a stationary listener at $30 \text{ m s}^{-1}$ ($v_{sound} = 340 \text{ m s}^{-1}$). (a) Calculate the observed frequency. (b) Calculate the wavelength in front of the moving ferry. (c) Compare with the Doppler-shift of ANSTO satellite radio at $2.2 \text{ GHz}, v = 7 \text{ km s}^{-1}$. [3+2+3 marks; ISMG: Knowledge and conceptual understanding, Analysis and interpretation]

• Cue. (a) $219 \text{ Hz}$; (b) $1.55 \text{ m}$; (c) $\Delta f/f \approx v/c = 2.3 \times 10^{-5}$, $\Delta f \approx 51 \text{ kHz}$.