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A-Level Wave properties, energy transfer by progressive waves and polarisation

What the A-Level syllabus expects for Wave properties, energy transfer by progressive waves and polarisation, and how to practise it.

What the syllabus expects

Understand that mechanical waves arise when particles oscillate inside a material medium like a taut string or a moving fluid, whereas electromagnetic waves are oscillations of the electromagnetic field across space and time
Grasp and apply this set of quantities: speed, wavelength, phase difference, phase, frequency, period, amplitude and displacement
Work out v = fλ starting from what speed, frequency and wavelength each mean
Use v = fλ from memory
Read and make sense of graphs of transverse and longitudinal waves plotted against either time or position
Understand that a travelling wave carries energy along while leaving the matter itself in place
Define intensity as a wave's radiated power spread over unit area, and use intensity ∝ (amplitude)² for a progressive wave
Understand and apply the fact that a wave leaving a point source with no energy loss thins in intensity as an inverse-square law
Recognise polarisation as an effect exclusive to transverse waves
Apply Malus' law to find the amplitude and intensity of plane-polarised light emerging from a polarising filter
Scope: intensity ∝ cos²θ

How it's examined

Questions on this topic most often ask you to explain, find. About 5% of the past-paper style questions in Rae's bank for this subject sit in this topic.

Worked examples

Example 1 (3 marks)

A source produces sound of frequency f and moves at a steady speed toward an observer who is at rest. The observer records the sound's frequency as f′. (a) With the help of a diagram, explain why f′ exceeds f.

Show the worked answer

Diagram: draw the source moving toward the observer, with the circular wavefronts (crests) it emits. Because the source advances after emitting each crest, the crests ahead of the source are bunched closer together, while those behind are spread out. Explanation: As the source moves toward the observer, each successive crest is emitted from a point nearer the observer, so the distance between consecutive crests reaching the observer (the observed wavelength) is shorter than the emitted wavelength. The sound still travels through the air at the fixed speed v (unaffected by the source's motion). Since v = f' x lambda' with v constant and lambda' reduced, the observed frequency f' = v/lambda' is increased, so f' > f.

Example 2 (2 marks)

(b) A source emits sound at a frequency f of 300 Hz. It travels at speed u m s⁻¹ directly toward a stationary listener, who detects a frequency f′ of 320 Hz. Taking the speed of sound in air as 340 m s⁻¹, find the source's speed u.