Year 9 Science | Victorian Curriculum 2.0
Waves & energy transfer through media
Topic 06 | Physical sciences | Answer key

Year 9 answers

Fluency

Types and properties

    1. (a) transverse, (b) longitudinal, (c) mostly transverse (water surface moves up/down), (d) transverse.
    2. Amplitude: max displacement from equilibrium. Frequency: cycles per second (Hz). Wavelength: distance between consecutive crests (m). Period: time for one full cycle (s).
    3. v=fλv = f \lambda: the speed of a wave equals its frequency multiplied by its wavelength.
    4. Radio -> microwave -> infrared -> visible -> ultraviolet -> X-ray -> gamma.
    5. Conduction (needs matter, best in solids), convection (needs fluid), radiation (no medium needed).
    6. Sound is a mechanical wave needing particles to vibrate. Vacuum has (almost) no particles, so no vibration can propagate.
Fluency

Wave equation calculations

    1. v=50×4=200v = 50 \times 4 = 200 m/s.
    2. λ=3×1082.4×109=0.125\lambda = \dfrac{3 \times 10^{8}}{2.4 \times 10^{9}} = 0.125 m =12.5= 12.5 cm.
    3. f=3×1083=1×108f = \dfrac{3 \times 10^{8}}{3} = 1 \times 10^{8} Hz = 100 MHz.
    4. f=v/λ=12/0.4=30f = v/\lambda = 12/0.4 = 30 Hz. Period T=1/30≈0.033T = 1/30 \approx 0.033 s.
    5. λ=1480/20=74\lambda = 1480/20 = 74 m.
    6. f=3×108/(650×10−9)≈4.6×1014f = 3 \times 10^{8} / (650 \times 10^{-9}) \approx 4.6 \times 10^{14} Hz.
Reasoning

Apply the ideas

    1. Low frequency = long wavelength. Diffraction is strongest when wavelength is similar to or larger than the obstacle/gap. Bass has wavelengths of metres, comparable to door widths, so it diffracts around corners. Treble has wavelengths of centimetres and diffracts much less.
    2. Microwaves: mobile phone signals, microwave ovens, radar. Infrared: TV remotes, thermal imaging. X-rays: medical imaging, airport security.
    3. UV photons carry more energy per photon and can ionise atoms or damage DNA directly, causing sunburn and skin cancer. Visible photons have less energy and are mostly absorbed harmlessly.
    4. Speed decreases (light is slower in water); wavelength decreases proportionally; frequency stays the same (set by the source).
    5. Incorrect. Sound travels faster in steel (rigid bonds transmit vibration quickly) than in air; “heavier” is the wrong factor — stiffness matters more than density.
Problem solving

Wave scenarios

    1. Distance =343×6≈2060= 343 \times 6 \approx 2060 m or about 22 km.
    2. λ=343/(40 000)=0.00858\lambda = 343 / (40\,000) = 0.00858 m ≈8.6\approx 8.6 mm. Short wavelength lets bats resolve small objects (insects) and focus the beam more tightly.
    3. v=fλ=2×1.5=3v = f\lambda = 2 \times 1.5 = 3 m/s. Time =25/3≈8.3= 25 / 3 \approx 8.3 s.
    4. AM wavelength =3×108/106=300= 3 \times 10^{8} / 10^{6} = 300 m, comparable to hills — diffracts well. FM wavelength =3×108/108=3= 3 \times 10^{8} / 10^{8} = 3 m, much smaller than hills — little diffraction, so FM needs line of sight.
Reasoning

Challenge

    1. Transverse waves cannot propagate through fluids because fluids have no shear rigidity. Observations show a “shadow zone” where S-waves do not arrive, meaning they pass through a liquid layer. P-waves still arrive (longitudinal, slower in liquid). This is evidence that the outer core is liquid.
    2. λ=1540/(3×106)≈5.1×10−4\lambda = 1540 / (3 \times 10^{6}) \approx 5.1 \times 10^{-4} m =0.51= 0.51 mm. Smallest resolvable feature is roughly the wavelength, so about 0.50.5 mm — enough to see an unborn baby’s bones and organs.
    3. Where waves from the two speakers arrive in phase (crests coincide), amplitudes add — loud (constructive interference). Where they arrive out of phase (crest meets trough), they cancel — quiet (destructive interference). The pattern depends on the path-length difference relative to wavelength.
    4. Pulse travels to target and back, total distance =c×t=3×108×1.2×10−4=3.6×104= c \times t = 3 \times 10^{8} \times 1.2 \times 10^{-4} = 3.6 \times 10^{4} m. Distance to target =1.8×104= 1.8 \times 10^{4} m =18= 18 km. Ideas used: EM waves travel at cc; distance = speed times time.
Year 9 Science study companion | Answer key