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Waves

7. Waves

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7. Waves — CAMBRIDGE AS & A LEVEL PHYSICS 9702 — COMPLETE NOTES notes: Describe and calculate with progressive waves, wave intensity, the c.r.o., transverse and longitudinal waves, the Doppler effect, the electromagnetic spectrum and polarisation.Progressive wave — a wave that tr…

  • Stationary wave
  • Direction of oscillation
  • Ripple tank
  • Displacement x
  • Amplitude A
  • Wavelength λ

Part 1 of 12Progressive waves

  • Progressive wavea wave that transfers energy from place to place without transferring matter; the particles just oscillate about fixed positions.
  • Stationary waveby contrast, it has fixed nodes and antinodes and transfers no net energy.
  • Direction of oscillationperpendicular to the direction of travel for transverse waves, parallel for longitudinal waves.
  • Ripple tankshows reflection, refraction and diffraction; shadows of the wavefronts are seen because the thicker water regions focus or block light.

Part 2 of 12Wave quantities

  • Displacement xdistance from the equilibrium position; a vector that can be positive or negative.
  • Amplitude Athe maximum displacement from equilibrium.
  • Wavelength λthe distance between two successive points in phase, e.g. crest to crest.
  • Period Tthe time for one complete oscillation; frequency f = 1/T, in hertz.
  • Wave speed vthe distance travelled by the wave per unit time.
  • Graph warningon a displacement–time graph the horizontal separation of identical points is the period; on a displacement–distance graph it is the wavelength.
  • Labellingarrows for wavelength and period go from a peak to the next peak, not near the crest.

Part 3 of 12Phase difference

  • Phase difference — how far one wave or point is ahead of or behind another, in fractions of a wavelength, degrees or radians.
    • In phase: 0 or 360° (2π rad), crests aligned.
    • Antiphase: 180° (π rad), crest aligned with trough.
    • Half a wavelength apart = 180°.
    • The wave that reaches a given displacement first leads; the other lags.

Part 4 of 12The cathode-ray oscilloscope

1C.R.O.2 points
— a laboratory instrument that displays waveforms of electrical signals against time (x-axis) and voltage (y-axis).
  • An a.c. signal appears as a transverse-looking wave from which amplitude and frequency can be found.
  • A d.c. voltage appears as a horizontal line at that voltage.
2Time-base3 points
— the time each division represents (e.g. 7 µs mm−1).
  • Count the horizontal length of one full wave on the screen.
  • Multiply by the time-base setting to get the period T.
  • Calculate f = 1/T, converting units carefully.

Part 5 of 12The wave equation

  • Derivationin one period T the wave travels one wavelength, so v = λ/T = fλ.
  • Wave equationv = fλ, for transverse and longitudinal waves (use c only for the speed of light).
    What the symbols mean: v = wave speed (m s−1) · f = frequency (Hz) · λ = wavelength (m)
  • Consequenceat constant speed, wavelength and frequency are inversely proportional.

Part 6 of 12Wave intensity

  • Intensitythe power transmitted per unit area perpendicular to the wave direction: I = P/A, in W m−2.
  • ProportionalityI ∝ A2 and I ∝ f2, so doubling the amplitude (or frequency) multiplies the intensity by 4.
  • Spherical wavesfrom a point source the energy spreads over a sphere of area 4πr2, so I ∝ 1/r2 (inverse square law), if no energy is absorbed.

Part 7 of 12Transverse and longitudinal waves

FeatureTransverseLongitudinal
Oscillation directionPerpendicular to energy transferParallel to energy transfer
StructurePeaks and troughsCompressions (high pressure) and rarefactions (low pressure)
Needs a medium?No, can travel through a vacuumYes, cannot travel through a vacuum
PolarisationCan be polarisedCannot be polarised
ExamplesElectromagnetic waves, guitar stringsSound waves
  • The wavelength of a longitudinal wave is the distance between successive compressions (or rarefactions).
  • A displacement–time graph for either kind looks the same, so read the question to decide the type.

Part 8 of 12Doppler effect for sound

1Doppler effect2 points
— the change in observed frequency due to relative motion between a source and an observer.
  • When the source moves towards the observer, the wavefronts are closer together (shorter wavelength), so the frequency and pitch are higher.
  • When it moves away, the wavelength is longer and the frequency and pitch are lower.
2Moving source equation3 points
— fo = fsv/(v ± vs).
  • Use v − vs when the source approaches.
  • Use v + vs when the source recedes.
  • The speed of sound in air is about 340 m s−1.

Part 9 of 12The electromagnetic spectrum

  • Common properties — all electromagnetic waves are transverse, travel in a vacuum at 3.00 × 108 m s−1, and can be reflected, refracted, diffracted, polarised and show interference.
  • Energy — higher frequency means higher photon energy; high-energy radiation (UV, X-rays, gamma) is ionising and harmful, whereas low-energy radiation is useful for communication.
RadiationWavelength range / m
Radio> 0.1
Microwaves0.1 to 1 × 10−3
Infrared1 × 10−3 to 7 × 10−7
Visible7 × 10−7 to 4 × 10−7
Ultraviolet4 × 10−7 to 1 × 10−8
X-rays1 × 10−8 to 4 × 10−13
Gamma rays4 × 10−13 to 10−16
  • Convert to frequency using c = fλ; for example microwaves are 3 × 109 to 3 × 1011 Hz.
  • Visible light spans 400 to 700 nm; some animals see infrared or ultraviolet.

Part 10 of 12Polarisation

  • Polarised wave — a transverse wave whose oscillations are restricted to a single plane (perpendicular to the direction of travel).
  • Unpolarised wave — oscillates in many planes.
    • An electromagnetic wave has electric and magnetic fields oscillating at right angles to each other and to the direction of travel.
  • Polariser — a filter with parallel slits that transmits only oscillations parallel to its transmission axis; a wave polarised perpendicular to the axis is completely blocked.
  • Evidence for transverse nature — polarisation only occurs for transverse waves (sound cannot be polarised).
  • Polaroid sunglasses — vertical transmission axes block horizontally polarised glare.
  • Metal grid — radio waves are polarised by passing through a metal grid.

Part 11 of 12Malus's law

  • Half rule — unpolarised light of intensity I0 passing through a polariser emerges polarised with intensity I0/2.
  • Analyser — a second polariser.
  • Malus's law — I = I0 cos2θ, where θ is the angle between the transmission axes and I0 is the intensity of the already polarised light.
    • θ = 0° or 180° gives maximum transmission (cos2θ = 1).
    • θ = 90° or 270° gives zero (cos2θ = 0).

Part 12 of 12More from the specification

  • OscilloscopeInstrument that displays electrical signals against time
  • VibrationA repeated backwards and forwards movement.
  • Cathode-ray oscilloscopeInstrument that displays voltage against time for electrical signals.

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