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Waves

A-Level Physics 9702 · Topic 7 revision notes · AS

Progressive waves and how to measure them, intensity, transverse and longitudinal waves, the Doppler effect, the electromagnetic spectrum and polarisation.

17 definitions to learn word for word, 11 equations in their own column, 9 diagrams and graphs. Read it, cover it, test yourself.

  1. 7.1a Progressive waves: describing a wave
  2. 7.1b Intensity and measuring waves with a CRO
  3. 7.2 Transverse and longitudinal waves
  4. 7.3 Doppler effect for sound waves
  5. 7.4 Electromagnetic spectrum
  6. 7.5 Polarisation
Definitions (mark-scheme wording)EquationsExam traps

7.1aProgressive waves: describing a wave

Definitions

Progressive wave
a wave that transfers energy from one place to another without transferring matter.
Displacement
the distance of a point on the wave from its equilibrium position (in a specified direction).
Amplitude
the maximum displacement of a particle from its equilibrium position.
Wavelength
the distance between two adjacent points on the wave that are in phase (e.g. crest to crest).
Period
the time taken for one complete oscillation of a point on the wave.
Frequency
the number of oscillations per unit time.
Phase difference
the fraction of a cycle (expressed as an angle) by which one oscillation leads or lags another.
Wave speed
the distance travelled by the wave (energy) per unit time.

Key points

  • Displacement-distance graph: crest-to-crest spacing = λ.
  • Displacement-time graph: crest-to-crest spacing = T.
  • One wavelength = 360° = 2π rad of phase; points λ/2 apart are in antiphase (180°).
  • Phase difference between two points = (x / λ) × 360°.
  • Derivation of v = fλ: the wave moves one wavelength in one period, v = λ/T = fλ.
yx / m λ A
Displacement against distance: the repeat length is the wavelength; A is measured from the equilibrium line.
PQR PQ: 90° PR: 180° S: in phase with P
Phase difference: P and Q are λ/4 apart (90°); P and R are λ/2 apart, in antiphase (180°); S is λ from P, in phase.

Watch out!

  • Check the horizontal axis: crest-to-crest on a time axis is T, not λ.
  • Amplitude is measured from the equilibrium line, not crest to trough.

7.1bIntensity and measuring waves with a CRO

Definitions

Intensity
the power transmitted per unit area (the area being perpendicular to the direction of travel of the wave).

Key points

  • Intensity is proportional to amplitude squared: double A gives 4 × I.
  • Cathode-ray oscilloscope: y-gain (V/div) sets the vertical scale; time-base (s/div) sets the horizontal scale.
  • Period from a CRO: T = (divisions for one cycle) × time-base setting; then f = 1/T.
  • Measure several cycles and divide, to reduce the percentage uncertainty.
  • Amplitude from a CRO: (divisions from centre to peak) × y-gain.
  • Speed of sound: two microphones to a CRO; move one until traces are back in phase; distance moved = λ, then v = fλ.
1 cycle = 4 div 2 ms / div
CRO trace, time-base 2 ms/div: one cycle spans 4 divisions, so T = 8 ms and f = 125 Hz.

Watch out!

  • Reading T from the CRO as the crest-to-trough spacing (that is only T/2).
  • I ∝ A2: halving the amplitude reduces intensity to a quarter, not a half.

7.2Transverse and longitudinal waves

Definitions

Transverse wave
a wave in which the particles oscillate perpendicular to the direction of energy transfer (wave travel).
Longitudinal wave
a wave in which the particles oscillate parallel to the direction of energy transfer (wave travel).
Compression / rarefaction
a region of a longitudinal wave where particles are closer together / further apart than normal (high / low pressure).

Key points

  • Transverse: all EM waves, waves on strings, water ripples, S-waves.
  • Longitudinal: sound, ultrasound, P-waves, compression pulses on a slinky.
  • Longitudinal waves need a medium; EM waves can travel through a vacuum.
  • Longitudinal wave: λ = distance between successive compressions.
  • Only transverse waves can be polarised: the test that tells them apart.
  • Displacement-distance graphs look sinusoidal for both types.
oscillation travel CC C RR oscillation transverse longitudinal
Transverse: oscillation perpendicular to travel. Longitudinal: oscillation parallel, forming compressions (C) and rarefactions (R).

Watch out!

  • A sine-shaped displacement graph does not prove a wave is transverse.
  • Saying sound particles travel with the wave: they only oscillate about fixed positions.

7.3Doppler effect for sound waves

Definitions

Doppler effect
the change in the observed frequency (and wavelength) of a wave when the source moves relative to the observer.

Key points

  • Moving source: wavefronts bunch up ahead and spread out behind; each is centred where the source was when emitted.
  • The wave speed in air is unchanged; only the observed wavelength and frequency change.
  • Source approaching: observed frequency higher (shorter λ).
  • Source receding: observed frequency lower (longer λ).
  • As a source passes, the heard pitch drops suddenly from high to low.
  • The equation is for a stationary observer and a moving source.
source vs ahead: higher f behind: lower f observer
Wavefronts from a source moving right: compressed ahead (higher f), stretched behind (lower f).
fo / Hzt / s fs approaching receding passes
Frequency heard by a stationary observer as a source passes at constant speed.

Watch out!

  • Sign error: approaching means v - vs in the denominator (answer larger than fs).
  • Saying the wave speed changes. It is the wavelength that changes.

7.4Electromagnetic spectrum

Definitions

Electromagnetic wave
a transverse wave of oscillating electric and magnetic fields that can travel through a vacuum at speed c.

Key points

  • Increasing frequency (decreasing λ): radio, microwave, infrared, visible, ultraviolet, X-ray, gamma.
  • All EM waves travel at c = 3.00 × 108 m s-1 in free space (almost the same in air).
  • All are transverse and can be polarised.
  • Visible light: 400 nm (violet) to 700 nm (red).
  • Approximate λ: radio > 10-1 m; microwave 10-3-10-1 m; infrared 7 × 10-7-10-3 m.
  • UV 10-8-4 × 10-7 m; X-ray 10-13-10-8 m; gamma 10-16-10-10 m (X and gamma overlap: named by origin).
radio micro IR UV X-ray γ visible 400-700 nm 10⁻¹ m 10⁻³ m 10⁻⁸ m λ increases f increases
The EM spectrum: wavelength decreases and frequency increases from radio to gamma.

Watch out!

  • Converting nm: 400 nm = 4 × 10-7 m, not 4 × 10-9 m.
  • Getting the order reversed: gamma has the highest frequency and shortest wavelength.

7.5Polarisation

Definitions

Plane-polarised wave
a transverse wave in which the oscillations occur in one plane only (containing the direction of travel).
Unpolarised wave
a transverse wave in which the oscillations occur in all planes perpendicular to the direction of travel.
Malus's law
the intensity transmitted by an analyser is I = I0 cos2θ, where θ is the angle between the plane of polarisation and the transmission axis.

Key points

  • Only transverse waves can be polarised; sound (longitudinal) cannot.
  • A polariser passes only the component of oscillation along its transmission axis.
  • Unpolarised light through one ideal polaroid: intensity halves.
  • Amplitude transmitted = A0 cos θ, so intensity (∝ A2) = I0 cos2θ.
  • Crossed polaroids (θ = 90°): no light transmitted.
  • Examples: light reflected from water or glass is partly polarised; microwaves from a transmitter are polarised (metal grille test).
polariser analyser I0 cos²θ unpolarised I0
Polariser then analyser at θ: vertical plane selected, then only the component along the analyser axis passes.
Iθ / ° I0 90 180 45°: I0/2
Malus's law: transmitted intensity against analyser angle; zero at 90°, full at 0° and 180°.

Watch out!

  • cos2θ is for intensity; amplitude uses cos θ.
  • Using I0 as the unpolarised intensity: after the first polariser it is already half that.
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