Lesson summary
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
Section 1 of 12Progressive waves
- Progressive wave
- a wave that transfers energy from place to place without transferring matter; the particles just oscillate about fixed positions.
- Stationary wave
- by contrast, it has fixed nodes and antinodes and transfers no net energy.
- Direction of oscillation
- perpendicular to the direction of travel for transverse waves, parallel for longitudinal waves.
- Ripple tank
- shows reflection, refraction and diffraction; shadows of the wavefronts are seen because the thicker water regions focus or block light.
Section 2 of 12Wave quantities
- Displacement x
- distance from the equilibrium position; a vector that can be positive or negative.
- Amplitude A
- the maximum displacement from equilibrium.
- Wavelength λ
- the distance between two successive points in phase, e.g. crest to crest.
- Period T
- the time for one complete oscillation; frequency f = 1/T, in hertz.
- Wave speed v
- the distance travelled by the wave per unit time.
- Graph warning
- on a displacement–time graph the horizontal separation of identical points is the period; on a displacement–distance graph it is the wavelength.
- Labelling
- arrows for wavelength and period go from a peak to the next peak, not near the crest.
Section 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.
Section 4 of 12The cathode-ray oscilloscope
1C.R.O.3 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-base4 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.
Section 5 of 12The wave equation
- Derivation
- in one period T the wave travels one wavelength, so v = λ/T = fλ.
- Wave equation
- v = fλ, for transverse and longitudinal waves.What the symbols mean: v = wave speed (m s−1) · f = frequency (Hz) · λ = wavelength (m)
- (use c only for the speed of light)
- v = fλ, for transverse and longitudinal waves.
- Consequence
- at constant speed, wavelength and frequency are inversely proportional.
Section 6 of 12Wave intensity
- Intensity
- the power transmitted per unit area perpendicular to the wave direction: I = P/A, in W m−2.What the symbols mean: I = intensity (W m−2) · P = power (W) · A = area the power falls on (m2)
- the power transmitted per unit area perpendicular to the wave direction: I = P/A, in W m−2.
- Proportionality
- I ∝ A2 and I ∝ f2, so doubling the amplitude (or frequency) multiplies the intensity by 4.
- Spherical waves
- from a point source the energy spreads over a sphere of area 4πr2, so I ∝ 1/r2 , if no energy is absorbed.
- (inverse square law)
- from a point source the energy spreads over a sphere of area 4πr2, so I ∝ 1/r2 , if no energy is absorbed.
Section 7 of 12Transverse and longitudinal waves
| Feature | Transverse | Longitudinal |
|---|---|---|
| Oscillation direction | Perpendicular to energy transfer | Parallel to energy transfer |
| Structure | Peaks and troughs | Compressions (high pressure) and rarefactions (low pressure) |
| Needs a medium? | No, can travel through a vacuum | Yes, cannot travel through a vacuum |
| Polarisation | Can be polarised | Cannot be polarised |
| Examples | Electromagnetic waves, guitar strings | Sound 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.
Section 8 of 12Doppler effect for sound
1Doppler effect3 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 equation4 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.
Section 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.
- all electromagnetic waves are transverse, travel in a vacuum at 3.00 × 108 m s−1,
- Energy
- higher frequency means higher photon energy; high-energy radiation is ionising and harmful,
- (UV, X-rays, gamma)
- whereas low-energy radiation is useful for communication.
- higher frequency means higher photon energy; high-energy radiation is ionising and harmful,
| Radiation | Wavelength range / m |
|---|---|
| Radio | > 0.1 |
| Microwaves | 0.1 to 1 × 10−3 |
| Infrared | 1 × 10−3 to 7 × 10−7 |
| Visible | 7 × 10−7 to 4 × 10−7 |
| Ultraviolet | 4 × 10−7 to 1 × 10−8 |
| X-rays | 1 × 10−8 to 4 × 10−13 |
| Gamma rays | 4 × 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.
Section 10 of 12Polarisation
- Polarised wave
- a transverse wave whose oscillations are restricted to a single plane.
- (perpendicular to the direction of travel)
- a transverse wave whose oscillations are restricted to a single plane.
- 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)
- polarisation only occurs for transverse waves.
- Polaroid sunglasses
- vertical transmission axes block horizontally polarised glare.
- Metal grid
- radio waves are polarised by passing through a metal grid.
Section 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).
Section 12 of 12More from the specification
- Oscilloscope
- Instrument that displays electrical signals against time
- Vibration
- A repeated backwards and forwards movement.
- Cathode-ray oscilloscope
- Instrument that displays voltage against time for electrical signals.
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