Waves

• A displacement–distance graph repeats every wavelength; a displacement–time graph repeats every period. Read the axis before you read the curve.
• Distance axis gives λ, time axis gives T. Intensity goes as amplitude squared. Approaching means minus. Malus squares the cosine, from the previous filter.

• 7.1.1 I can describe — describe what is meant by wave motion as illustrated by vibration in ropes, springs and ripple tanks
• 7.1.2 I can understand — understand and use the terms displacement, amplitude, phase difference, period, frequency, wavelength and speed
• 7.1.3 I can understand — understand the use of the time-base and y-gain of a cathode-ray oscilloscope (CRO) to determine frequency and amplitude
• 7.1.4 I can — derive, using the definitions of speed, frequency and wavelength, the wave equation v = fλ
• 7.1.5 I can recall — recall and use v = fλ
• 7.1.6 I can understand — understand that energy is transferred by a progressive wave
• 7.1.7 I can recall — recall and use intensity = power/area and intensity ∝ (amplitude)² for a progressive wave
• 7.2.1 I can compare — compare transverse and longitudinal waves
• 7.2.2 I can — analyse and interpret graphical representations of transverse and longitudinal waves
• 7.3.1 I can understand — understand that when a source of sound waves moves relative to a stationary observer, the observed frequency is different from the source frequency (understanding of the Doppler effect for a stationary source and a moving observer is not required)
• 7.3.2 I can use — use the expression f_o = f_s v / (v ± v_s) for the observed frequency when a source of sound waves moves relative to a stationary observer
• 7.4.1 I can state — state that all electromagnetic waves are transverse waves that travel with the same speed c in free space
• 7.4.2 I can recall — recall the approximate range of wavelengths in free space of the principal regions of the electromagnetic spectrum from radio waves to γ-rays
• 7.4.3 I can recall — recall that wavelengths in the range 400–700 nm in free space are visible to the human eye
• 7.5.1 I can understand — understand that polarisation is a phenomenon associated with transverse waves
• 7.5.2 I can recall — recall and use Malus's law (I = I₀ cos²θ) to calculate the intensity of a plane-polarised electromagnetic wave after transmission through a polarising filter or a series of polarising filters (calculation of the effect of a polarising filter on the intensity of an unpolarised wave is not required)

What moves along is energy and the pattern, not the medium. A cork on a pond bobs up and down as ripples pass; it is not carried to the bank. A leaf does not travel with a sound wave. That is the whole meaning of "progressive": the disturbance progresses, the medium does not.

• “The repeat length on a wave graph is the wavelength.” Correct Only if the horizontal axis is distance. A displacement–distance graph gives \(\lambda\); a displacement–time graph gives \(T\). The two look identical; the axis label is the only difference.
• “Amplitude is the height from trough to crest.” Correct That is twice the amplitude. Amplitude is the maximum displacement from the equilibrium position. On a CRO, halve the crest-to-trough height before multiplying by the y-gain.
• “Divisions × time-base gives the frequency.” Correct It gives the period, \(T\). The frequency is \(1/T\).
• “Doubling the amplitude doubles the intensity.” Correct Intensity \(\propto \text{amplitude}^2\), so it quadruples.
• “For a source coming towards you, use \(v + v_s\).” Correct Approaching means a higher observed frequency, so the denominator must be smaller: \(v - v_s\). Receding: \(v + v_s\). Check the answer against the pitch you would hear.
• “\(I = I_0\cos\theta\).” Correct The filter passes \(\cos\theta\) of the amplitude; intensity goes as amplitude squared, so \(I = I_0\cos^2\theta\). In a chain of filters, \(\theta\) is measured from the axis of the previous filter.
• “At a compression the particles have their largest displacement.” Correct The particle at the centre of a compression has zero displacement; its neighbours on either side are displaced towards it.
• “The particles of the medium travel along with the wave.” Repair They oscillate about fixed equilibrium positions. A progressive wave transfers energy, not matter.
• “Amplitude is the height from a trough to a crest.” Repair That is twice the amplitude. Amplitude is the maximum displacement from the equilibrium position.
• “Wavelength is the distance from a crest to the next trough.” Repair That is \(\lambda/2\). Wavelength is the distance between adjacent points in phase, such as crest to crest.
• “I read the period off the displacement–distance graph.” Repair That graph repeats every wavelength. The period comes from a displacement–time graph.
• “On the CRO, frequency = divisions × time-base.” Repair That product is the period, \(T\). Then \(f = 1/T\).
• “A higher frequency makes the sound travel faster.” Repair The medium sets the speed. In the same air a higher frequency means a shorter wavelength, at the same speed.
• “Doubling the amplitude doubles the intensity.” Repair \(I \propto x_0^2\), so it quadruples.
• “At a compression the particle displacement is largest.” Repair The particle at the centre of a compression has zero displacement; the particles on either side are displaced towards it.
• “The approaching ambulance's siren emits a higher frequency.” Repair It emits \(f_s\) throughout. The wavelength reaching the observer ahead is shorter, so the observed frequency is higher.
• “For an approaching source use \(v + v_s\).” Repair \(v - v_s\): the smaller denominator gives the higher observed frequency that an approaching source must produce.
• “Radio waves travel more slowly than light in a vacuum.” Repair Every electromagnetic wave travels at \(c = 3.00 \times 10^8\,\mathrm{m\,s^{-1}}\) in free space.
• “X-rays and γ-rays are told apart by their wavelength.” Repair Their ranges overlap. They differ in origin: γ-rays come from unstable nuclei, X-rays from outside the nucleus.
• “Sound cannot be polarised because it is too slow.” Repair Sound is longitudinal: it oscillates along its direction of travel, so there is no plane across the travel for a filter to select.
• “\(I = I_0\cos\theta\).” Repair The amplitude is multiplied by \(\cos\theta\); intensity \(\propto \text{amplitude}^2\), so \(I = I_0\cos^2\theta\).
• “The second filter is at 90° to the original plane, so nothing gets through.” Repair In a series, \(\theta\) is measured from the previous filter's axis. If the first filter is at 30°, the second is at 60° to it, and a quarter of the light leaving the first filter gets through.

• Read the command word before you decide how much to write. This syllabus has fifteen of them: calculate, comment, compare, define, describe, determine, explain, give, identify, justify, predict, show (that), sketch, state and suggest. Define wants a precise meaning — for a physical quantity, usually an equation in words with every quantity named. State and give want a fact and nothing more. Describe wants the points or the features. Explain wants the reasons and the relationships — a describe-level answer to an explain question is incomplete however well written it is. Show (that) gives you the result and asks for the structured evidence that leads to it, so every step must appear — and a final value worked to one more significant figure than the one printed makes it plain that you calculated it rather than copied it. Sketch wants a freehand graph with its key features — intercepts, asymptotes, the shape — correct, but no plotted scale.
• Precision on a CRO is about using more of the screen. Measure across as many whole cycles as fit and divide: 4 cycles over 8.0 divisions, read to ±0.1 division, has a quarter of the percentage uncertainty of 1 cycle over 2.0 divisions. For the same reason choose a time-base at which the whole cycles you measure span most of the screen's width, and the y-gain that makes the trace as tall as the screen allows. Changing either setting changes the picture, not the signal: the period and amplitude you calculate stay the same.
• "Show that" wants every link. An answer that writes "\(v = s/t\), \(s = \lambda\), \(t = T\), so \(v = f\lambda\)" has skipped the physics: it must say why the distance in one period is one wavelength. That sentence is the derivation; the algebra is one line.
• "Compare" means both sides of each point. "Transverse waves oscillate at 90° to the direction of travel" is half a comparison. Write the pair: "transverse perpendicular, longitudinal parallel, to the direction of energy transfer". The command word asks for similarities and/or differences, so a similarity earns credit too.
• "Explain why sound cannot be polarised" needs the chain in full: sound is longitudinal; its oscillations are parallel to the direction of travel; so there is no plane of oscillation across the direction of travel for a filter to select. "Because it is longitudinal" alone states the fact without the reason.
• Interleave with the chapters that use this one. Topic 8 (Superposition) builds on phase difference and wavelength: when you reach it, re-answer "what phase difference do two points half a wavelength apart have?". Topic 17 (Oscillations) treats one particle's motion as simple harmonic motion: re-draw a displacement–time graph. Topic 24 (Medical physics) uses intensity for X-rays and sound, and Topic 25 (Astronomy and cosmology) the Doppler idea for light: re-state intensity = power/area and the Doppler sign rule first. Recalling a topic inside a new context is worth more than another pass over this chapter on its own; at A Level, Paper 4 assumes the whole of the AS content, so nothing here is ever finished with.

• Cambridge International AS & A Level Physics 9702 has five components. Topic 7 is AS Level content, so it is examined in Papers 1, 2 and 3. AS Level content: examined in Paper 1 (multiple choice), Paper 2 (AS structured) and, as practical context, Paper 3. Assumed knowledge for Papers 4 and 5. AS Level candidates take Papers 1, 2 and 3; A Level candidates take all five, either staged over two years (Papers 1–3 in year one, Papers 4 and 5 in year two) or together in one series. Examinations are available in the June and November series, and in March in India.
• Across both the AS Level and the A Level the assessment objectives are weighted AO1 40% (knowledge and understanding), AO2 40% (handling, applying and evaluating information) and AO3 20% (experimental skills and investigations). AS candidates are graded a–e; A Level candidates A*–E. The Data and formulas sheet is printed as page 2 of Papers 1 and 2 and as pages 2 and 3 of Paper 4: it gives the constants and a short list of formulas. Every other equation in this chapter is one the syllabus says you must recall, and this chapter says which is which.
• A Paper 1 item on waves can turn on a single distinction: amplitude or peak-to-peak, period or wavelength read from the wrong graph, \(\cos\theta\) or \(\cos^2\theta\), \(v - v_s\) or \(v + v_s\). A Paper 2 question asks you to define a wave term, compare transverse and longitudinal waves, show that \(v = f\lambda\), explain the Doppler effect from wavefronts, or explain why polarisation shows that light is transverse.
• Period and amplitude from a CRO trace; \(v = f\lambda\); phase difference from a separation; intensity from power and area, and its change with amplitude; the observed frequency from a moving source; the intensity through one or more polarising filters. Only the Doppler expression and \(c\) are on the Data and formulas sheet; \(v = f\lambda\), intensity \(=\) power/area, \(I \propto x_0^2\) and Malus's law are recall.
• Paper 3 uses the CRO and signal generator as instruments: here, the speed of sound from two microphones and a double-beam CRO, with the frequency varied, five wavelengths measured on a metre rule, and \(v\) from the gradient of \(\lambda\) against \(1/f\). The largest uncertainty is judging when the traces are in phase. Paper 5 can ask you to plan a test of Malus's law and analyse the readings.
• Read the command word before you decide how much to write. This syllabus has fifteen of them: calculate, comment, compare, define, describe, determine, explain, give, identify, justify, predict, show (that), sketch, state and suggest. Define wants a precise meaning — for a physical quantity, usually an equation in words with every quantity named. State and give want a fact and nothing more. Describe wants the points or the features. Explain wants the reasons and the relationships — a describe-level answer to an explain question is incomplete however well written it is. Show (that) gives you the result and asks for the structured evidence that leads to it, so every step must appear — and a final value worked to one more significant figure than the one printed makes it plain that you calculated it rather than copied it. Sketch wants a freehand graph with its key features — intercepts, asymptotes, the shape — correct, but no plotted scale.