Waves

• If you are not sure which route you are on, ask before you revise. Learning Supplement material you will not be examined on costs time you do not have; missing it when you are entered for Extended costs marks that are there for the taking. Your centre knows which papers you are entered for. Confirm your entry route, then mark this page accordingly.
• Three anchors that prevent most lost marks. (1) The source fixes the frequency — crossing a boundary changes \(v\) and \(\lambda\), never \(f\). (2) Every optical angle is measured between the ray and the normal, never the surface. (3) An echo goes there and back, so the one-way distance is \(\dfrac{vt}{2}\). Say all three from memory before you read on.
• Three sentences that between them prevent most of the losses above. (1) Every angle is measured from the normal. (2) The source owns the frequency; a boundary changes \(v\) and \(\lambda\). (3) If the pulse came back, halve the time. Say all three from memory before you start section 3.1.
• Section 3.1 in one line. Energy travels, matter does not; \(v = f\lambda\) links the three measurements; the source owns the frequency; and every wave reflects, refracts and diffracts. Close the page and write those four clauses from memory.
• Section 3.2.1 in one line. Normal first, dashed, at 90° to the surface; \(i = r\) measured from it; and a plane-mirror image is virtual, same size, and as far behind as the object is in front.
• Never reverse these two. Short sight focuses short of the retina, so the correction must push the focus back — only a diverging lens does that. Long sight would focus long, beyond the retina, so the correction must pull the focus forward — only a converging lens does that. Short → diverging. Long → converging.
• Order it once, use it twice. Red, Orange, Yellow, Green, Blue, Indigo, Violet runs from lowest frequency and longest wavelength to highest frequency and shortest wavelength. Reverse the list and you have it in order of increasing wavelength. Frequency and wavelength always run in opposite directions, because \(v = f\lambda\) with \(v\) fixed.
• The four improvements that fit almost every optics practical here. Thin pencil lines · ray marks widely separated · view scales from directly above to avoid parallax · repeat each angle and average. For the sound practicals, substitute: increase the distance · time many events and divide · use electronic timing · work in still air.

• I know that waves transfer energy without transferring matter. Core 3.1.1
• I can describe wave motion as illustrated by vibrations in ropes and springs, and by experiments using water waves. Core 3.1.2
• I can describe the features of a wave in terms of wavefront, wavelength, frequency, crest (peak), trough, amplitude and wave speed. Core 3.1.3
• I can recall and use the equation for wave speed, \(v = f\lambda\). Core 3.1.4
• I know that for a transverse wave the direction of vibration is at right angles to the direction of propagation, and that electromagnetic radiation, water waves and seismic S-waves can be modelled as transverse. Core 3.1.5
• I know that for a longitudinal wave the direction of vibration is parallel to the direction of propagation, and that sound waves and seismic P-waves can be modelled as longitudinal. Core 3.1.6
• I can describe how waves can undergo reflection at a plane surface, refraction due to a change of speed, and diffraction through a narrow gap. Core 3.1.7
• I can describe the use of a ripple tank to show reflection at a plane surface, refraction due to a change in speed caused by a change in depth, diffraction due to a gap and diffraction due to an edge. Core 3.1.8
• I can define and use the terms normal, angle of incidence and angle of reflection. Core 3.2.1.1
• I can describe the formation of an optical image by a plane mirror and give its characteristics: same size, same distance from the mirror, virtual. Core 3.2.1.2
• I can state that for reflection the angle of incidence equals the angle of reflection, and I can recall and use that relationship. Core 3.2.1.3
• I can define and use the terms normal, angle of incidence and angle of refraction. Core 3.2.2.1
• I can describe an experiment to show refraction of light by transparent blocks of different shapes. Core 3.2.2.2
• I can describe the passage of light through a transparent material, limited to the boundaries between two mediums only. Core 3.2.2.3
• I can state the meaning of critical angle. Core 3.2.2.4
• I can describe internal reflection and total internal reflection using both experimental and everyday examples. Core 3.2.2.5
• I can describe the action of thin converging and thin diverging lenses on a parallel beam of light. Core 3.2.3.1
• I can define and use the terms focal length, principal axis and principal focus (focal point). Core 3.2.3.2
• I can draw and use ray diagrams for the formation of a real image by a converging lens. Core 3.2.3.3
• I can describe the characteristics of an image using the terms enlarged / same size / diminished, upright / inverted and real / virtual. Core 3.2.3.4
• I know that a virtual image is formed when diverging rays are extrapolated backwards, and that it does not form a visible projection on a screen. Core 3.2.3.5
• I can describe the dispersion of light as illustrated by the refraction of white light by a glass prism. Core 3.2.4.1
• I know the traditional seven colours of the visible spectrum in order of frequency and in order of wavelength. Core 3.2.4.2
• I know the main regions of the electromagnetic spectrum in order of frequency and in order of wavelength. Core 3.3.1
• I know that all electromagnetic waves travel at the same high speed in a vacuum. Core 3.3.2
• I can describe typical uses of each region of the electromagnetic spectrum, from radio waves to gamma rays. Core 3.3.3
• I can describe the harmful effects on people of excessive exposure to electromagnetic radiation, region by region. Core 3.3.4
• I know that communication with artificial satellites is mainly by microwaves, and I can distinguish the low-orbit and geostationary uses. Core 3.3.5
• I can describe the production of sound by vibrating sources. Core 3.4.1
• I can describe the longitudinal nature of sound waves. Core 3.4.2
• I can state the approximate range of frequencies audible to humans as 20 Hz to 20 000 Hz. Core 3.4.3
• I know that a medium is needed to transmit sound waves. Core 3.4.4
• I know that the speed of sound in air is approximately 330–350 m/s. Core 3.4.5
• I can describe a method involving a measurement of distance and time for determining the speed of sound in air. Core 3.4.6
• I can describe how changes in amplitude and frequency affect the loudness and pitch of sound waves. Core 3.4.7
• I can describe an echo as the reflection of sound waves. Core 3.4.8
• I can define ultrasound as sound with a frequency higher than 20 kHz. Core 3.4.9
• I can describe how wavelength and gap size affect diffraction through a gap. Supplement 3.1.9
• I can describe how wavelength affects diffraction at an edge. Supplement 3.1.10
• I can use simple constructions, measurements and calculations for reflection by plane mirrors. Supplement 3.2.1.4
• I can define refractive index, \(n\), as the ratio of the speeds of a wave in two different regions. Supplement 3.2.2.6
• I can recall and use the equation \(n = \dfrac{\sin i}{\sin r}\). Supplement 3.2.2.7
• I can recall and use the equation \(n = \dfrac{1}{\sin c}\). Supplement 3.2.2.8
• I can describe the use of optical fibres, particularly in telecommunications. Supplement 3.2.2.9
• I can draw and use ray diagrams for the formation of a virtual image by a converging lens. Supplement 3.2.3.6
• I can describe the use of a single lens as a magnifying glass. Supplement 3.2.3.7
• I can describe the use of converging and diverging lenses to correct long-sightedness and short-sightedness. Supplement 3.2.3.8
• I can recall that visible light of a single frequency is described as monochromatic. Supplement 3.2.4.3
• I know that the speed of electromagnetic waves in a vacuum is \(3.0 \times 10^{8}\) m/s, and is approximately the same in air. Supplement 3.3.6
• I know that many important communications systems rely on electromagnetic radiation: mobile phones and wireless internet on microwaves, Bluetooth on radio waves, and optical fibres on visible light or infrared. Supplement 3.3.7
• I know the difference between a digital and an analogue signal. Supplement 3.3.8
• I know that a sound can be transmitted as a digital or an analogue signal. Supplement 3.3.9
• I can explain the benefits of digital signalling, including an increased rate of data transmission and increased range through accurate signal regeneration. Supplement 3.3.10
• I can describe compression and rarefaction. Supplement 3.4.10
• I know that, in general, sound travels faster in solids than in liquids and faster in liquids than in gases. Supplement 3.4.11
• I can describe the uses of ultrasound in non-destructive testing of materials, medical scanning of soft tissue and sonar, including calculating depth or distance from time and wave speed. Supplement 3.4.12

Why it matters: the normal convention introduced here is used for the rest of the chapter — refraction, critical angle, total internal reflection and lens work all measure from the normal. An answer that measures from the surface instead will be wrong in 3.2.2 for exactly the same reason it is wrong here, so fix the habit now.

• 1. “Waves transport particles from the source to the receiver.” Core 3.1.1 Why wrongA floating bottle is not delivered to the beach by the first wave, and a shout produces no wind. Nothing arrives except energy. CorrectEach particle oscillates about a fixed equilibrium position and returns to it; the pattern of displacement advances, carrying energy. Say this“A wave transfers energy without transferring matter; the particles oscillate about fixed equilibrium positions.” CheckDescribe the motion of a cork as ripples pass it, and state what has been transferred past it.
• 2. “Amplitude is the distance from crest to trough.” Core 3.1.3 Why wrongThat distance spans the full swing, from one extreme to the other, so it is twice the maximum displacement from the middle. CorrectAmplitude is measured from the equilibrium (mean) line to a crest, or from the mean line to a trough. Crest-to-trough is \(2a\). Say this“Amplitude is the maximum distance from the mean position.” CheckA trace shows a crest 6 cm above a trough. State the amplitude. (3 cm.)
• 3. “Particles in a longitudinal wave follow a sinusoidal path.” Core 3.1.6 Why wrongThe smooth curve drawn for a longitudinal wave is a graph of pressure or displacement against position, not a picture of a particle’s trajectory. CorrectEach particle moves back and forth along a straight line, parallel to the direction of energy transfer. Say this“In a longitudinal wave the particles vibrate parallel to the direction of energy transfer; the curve is a graph, not a path.” CheckSound travels east. State the direction in which an air molecule oscillates.
• 4. “Frequency changes when a wave crosses a boundary.” Core 3.1.7 Why wrongIf fewer crests left the boundary each second than arrived at it, crests would have to pile up there without limit. They do not. CorrectFrequency is fixed by the source. Speed changes at the boundary, and since \(v = f\lambda\) with \(f\) fixed, the wavelength changes in the same ratio. Say this“The frequency is unchanged because it is determined by the source; the speed and wavelength both change.” CheckA 500 Hz sound passes from air into water where it travels about four times faster. State what happens to \(f\) and to \(\lambda\).
• 5. “Refraction occurs because the amplitude changes.” Core 3.1.7 Why wrongAmplitude controls how much energy the wave carries. It has no influence on direction; a very quiet and a very loud sound refract identically. CorrectRefraction is caused by a change of speed. A wavefront arriving obliquely pivots because one end slows before the other. Say this“Refraction occurs because the wave changes speed at the boundary.” CheckState the one quantity whose change causes refraction.
• 6. “Diffraction is greatest through a very wide gap.” Supplement 3.1.9 Why wrongIt confuses how much energy gets through with how much the wave spreads. A wide gap passes plenty of energy, almost straight on. CorrectSpreading depends on the ratio of wavelength to gap width and is greatest when the gap is comparable to the wavelength. Say this“Diffraction is most noticeable when the gap width is about the same as the wavelength.” CheckWaves of wavelength 2 cm meet a gap. Which gives more spreading, 2 cm or 20 cm?
• 7. “Angles in optics are measured from the surface.” Core 3.2.1.1 Why wrongEvery optical law in this topic is defined with respect to the normal — \(i = r\) for all candidates, and \(n = \sin i / \sin r\) and \(n = 1/\sin c\) for Extended candidates. Measuring from the surface gives the complement, \(90^\circ - i\). CorrectDraw the dashed normal at 90° to the surface at the point of incidence first, then measure every angle from it. Say this“The angle of incidence is the angle between the incident ray and the normal.” CheckA ray strikes a mirror at 25° to the surface. State the angle of reflection. (65°.)
• 8. “A plane-mirror image lies on the mirror.” Core 3.2.1.2 Why wrongTo photograph your reflection sharply, a camera must focus on a point twice your distance from the glass, not on the glass surface. CorrectThe image is the same perpendicular distance behind the mirror as the object is in front, on the line perpendicular to the mirror through the object. Say this“The image is formed the same perpendicular distance behind the mirror as the object is in front of it.” CheckA person stands 1.2 m from a mirror. How far is the person from the image? (2.4 m.)
• 9. “A virtual image can be projected onto a screen.” Core 3.2.3.5 Why wrongNo light actually reaches the virtual image position, so there is nothing for a screen to intercept. CorrectOnly a real image, where rays genuinely cross, can be formed on a screen. A virtual image is formed by backward extensions of diverging rays. Say this“The image is virtual, so no light passes through it and it cannot be formed on a screen.” CheckName one virtual image you can see right now, and say why a screen would show nothing.
• 10. “Light always bends when it crosses a boundary.” Core 3.2.2.3 Why wrongBending needs an oblique wavefront so that one end slows before the other. A wavefront arriving square-on slows all at once. CorrectAt normal incidence (\(i = 0^\circ\)) the speed and wavelength change but the direction does not. Say this“A ray travelling along the normal is not deviated, although its speed and wavelength do change.” CheckWhy is a ray aimed at the centre of the flat face of a semicircular block not bent at the curved surface?
• 11. “The critical angle works in either travel direction.” Core 3.2.2.5 Why wrongLight entering a denser medium bends towards the normal, so the angle inside can never reach 90°; there is nothing for a critical angle to mark. CorrectThe critical angle is defined for light travelling from higher refractive index to lower. Say this“The critical angle is the angle of incidence in the denser medium for which the angle of refraction is 90°.” CheckDoes a ray going from air into glass have a critical angle? (No.)
• 12. “Total internal reflection occurs at the critical angle.” Core 3.2.2.5 Why wrongAt exactly \(c\) a refracted ray still exists — it travels along the boundary at 90° to the normal. CorrectTotal internal reflection needs the angle of incidence to be strictly greater than \(c\). Say this“Total internal reflection occurs when the angle of incidence is greater than the critical angle.” CheckWater has \(c = 49^\circ\). A ray inside the water strikes the surface at 49°. What happens?
• 13. “A converging lens always produces a real image.” Supplement 3.2.3.6 Why wrongEvery magnifying glass disproves it. With the object inside the focal length the emerging rays still diverge, so they never cross. CorrectReal image only when the object is further from the lens than F. Inside F the image is virtual, upright and magnified. Say this“With the object inside the focal length, the emerging rays diverge and the image is virtual, upright and magnified.” Check\(f = 10\) cm and the object is 6 cm from the lens. Real or virtual? Upright or inverted?
• 14. “A diverging lens corrects long-sightedness.” Supplement 3.2.3.8 Why wrongA long-sighted eye converges light too weakly already; spreading the rays further pushes the focus even further behind the retina. CorrectLong sight needs extra convergence, so it takes a converging lens. Short sight needs less, so it takes a diverging lens. Say this“A converging lens corrects long sight by bringing the rays together before they enter the eye, so the image forms on the retina.” CheckSomeone can read comfortably but cannot read a road sign. Which lens do they need?
• 15. “A prism creates the colours.” Core 3.2.4.1 Why wrongIsolate one colour and send it through a second prism: it stays that colour. Nothing new is manufactured. CorrectWhite light is already a mixture of frequencies; the prism separates them because glass refracts each frequency by a slightly different amount. Say this“The prism separates the colours already present in white light, because the refractive index of glass is slightly different for each frequency.” CheckWhat is seen if a second, inverted prism is placed after the first?
• 16. “Radio waves are sound waves.” Core 3.3.1 Why wrongA radio wave is transverse, electromagnetic, travels at the same high speed in a vacuum as every other electromagnetic wave, and crosses a vacuum. Sound is longitudinal, mechanical, travels at a few hundred metres per second and cannot cross a vacuum. CorrectA radio receiver converts the radio wave it detects into an electrical signal and then into sound. The two waves are different at every level. Say this“Radio waves are transverse electromagnetic waves; sound waves are longitudinal mechanical waves that need a medium.” CheckGive two differences between a radio wave and a sound wave.
• 17. “Electromagnetic waves need a medium.” Core 3.3.2 Why wrongSunlight reaches Earth across 150 million kilometres of near-vacuum. If a medium were needed, the sky would be dark. CorrectElectromagnetic waves are oscillating electric and magnetic fields and travel through a vacuum at the same high speed, whatever the region. Say this“Electromagnetic waves do not require a material medium and all travel at the same high speed in a vacuum.” Extended candidates may add the value, \(3.0 \times 10^{8}\) m/s (Supplement 3.3.6); Core answers do not need it. CheckAstronauts on a spacewalk can see each other but must use radios to talk. Explain both facts.
• 18. “All electromagnetic waves are equally dangerous.” Core 3.3.4 Why wrongThe hazard depends on frequency, intensity and exposure time. Radio waves at everyday intensities have no measurable effect; gamma rays ionise molecules in cells. CorrectExcessive exposure to any region heats tissue and can burn. Ultraviolet, X-rays and gamma rays are additionally ionising: ultraviolet damages surface cells and the eyes, leading to skin cancer and eye conditions, and X-rays and gamma rays cause mutation or damage to cells in the body. Say this“Excessive exposure to any electromagnetic radiation can heat tissue and cause burns, but only ultraviolet, X-rays and gamma rays are ionising.” CheckState one hazard of microwaves and one of gamma rays, and say which is ionising.
• 19. “Pitch depends on amplitude.” Core 3.4.7 Why wrongPlay the same guitar string harder: it sounds louder, not higher. The note is unchanged. CorrectPitch is set by frequency. Higher frequency gives higher pitch. Say this“A higher frequency gives a higher pitch.” CheckTwo traces have the same height but one has twice as many waves. Which sound is higher in pitch?
• 20. “Loudness depends on frequency.” Core 3.4.7 Why wrongThe mirror image of the previous error. A high whistle can be barely audible and a low drum deafening. CorrectLoudness is set mainly by amplitude. Greater amplitude gives a louder sound. Say this“A larger amplitude gives a louder sound.” CheckWhich measurement on a waveform display tells you the loudness?
• 21. “Sound travels fastest in gases.” Supplement 3.4.11 Why wrongIt reverses the particle argument. Gas particles are far apart and interact only on collision, so a disturbance crosses a gas slowly. CorrectSound travels fastest in solids, more slowly in liquids, and slowest in gases, because closely packed and strongly bonded particles pass the disturbance on more quickly. Say this“In general, sound travels faster in solids than in liquids and faster in liquids than in gases.” CheckPut air, sea water and steel in order of increasing speed of sound.
• 22. “Ultrasound means very loud sound.” Core 3.4.9 Why wrongIt confuses the two axes of a trace. “Ultra” here refers to frequency, not amplitude. A dog whistle is ultrasonic and very quiet. CorrectUltrasound is sound of frequency above 20 kHz, beyond the upper limit of human hearing. Its loudness is a separate matter entirely. Say this“Ultrasound is sound with a frequency higher than 20 kHz.” CheckIs a 30 kHz sound necessarily loud? Explain.
• 23. “Echo distance is \(vt\).” Core 3.4.8 Why wrong\(vt\) is the total distance the pulse travelled, and the pulse went to the reflector and back. It covered the gap twice. CorrectWrite \(2d = vt\) first, then rearrange to \(d = \dfrac{vt}{2}\). Say this“The pulse travels to the reflector and back, so the distance to the reflector is \(vt/2\).” CheckAn echo returns after 1.2 s with \(v = 340\) m/s. How far away is the wall? (204 m.)

• The tier is always readable from the words. Every tag begins with the word Core or Supplement, and every Supplement block carries a written heading. Nothing on this page relies on colour to tell you which route content belongs to, so it reads correctly in dark mode, in greyscale print and on a monochrome reader.
• How to use these lists. The verbs are the syllabus verbs. “Know” and “state” outcomes need a memorised sentence. “Define” outcomes need the precise wording. “Describe” outcomes need an ordered set of points, usually four to six. “Draw” outcomes need a construction you can produce with a ruler in under three minutes. “Explain” outcomes need a reason in every sentence. Practise them in that form, not as continuous prose.
• Reading the tier column. Ten of the fifty-six statements sit in 3.1, twenty-one across the four light subsections, ten in 3.3 and twelve in 3.4. The Supplement statements are not spread evenly: 3.2.2 and 3.3 each carry four or five, so those two subsections are where an Extended candidate has the most extra ground to cover.
• Route and paper are not interchangeable. Paper numbers in Physics 0625 mean what the table above says and nothing else. If a past-paper question is labelled for a component you are not sitting, it may test content outside your route — check the tier tag on the topic before you spend time on it.
• Answering “state the difference”. A difference needs both halves and a stated reference direction. “Transverse vibrates up and down” states nothing on its own, because up and down is meaningless without saying what it is relative to. Write: “In a transverse wave the vibration is at right angles to the direction of propagation; in a longitudinal wave the vibration is parallel to it.” The syllabus wording is direction of propagation, so use that phrase rather than “direction of energy transfer” when the question asks for the definition.
• Answering “what does monochromatic mean?” Say light of a single frequency. “One colour” is the translation of the word, not the physics, and on its own it is unlikely to score. If the question then asks what happens when monochromatic light enters a prism, the answer is that it is refracted but not dispersed, because there is only one frequency to separate.
• How to answer “why is this region used for that?”. Name the physical property, then the consequence. “Microwaves are used for satellite links because they pass through the atmosphere without being strongly absorbed, so the signal reaches the satellite and returns.” A bare statement of the use, with no property named, does not answer the question that was asked, and a property left unconnected to the use answers only half of it.
• Say “regenerated”, not “amplified”. Supplement 3.3.10 asks for the benefit to be explained, and the explanation is that the pulses are rebuilt because only two states have to be recognised. An answer that says the signal is “made stronger” describes amplification, which an analogue signal gets too, and so does not explain any advantage at all.
• Check your own diagram in twenty seconds. Run these four questions: Is every normal dashed and perpendicular? Does every real ray have an arrowhead? Are all virtual lines dashed? Does the image type (real/virtual, upright/inverted) match what the construction actually shows, rather than what you expected? Four yeses means the diagram is internally consistent and says what you meant it to say.
• The improvement rule. “Be more careful”, “use better apparatus” and “repeat and average” on their own are not improvements — they name no specific change. A usable improvement names the measurement, the change and the effect: “mark the ray with two crosses at least 8 cm apart, because a longer baseline makes the drawn line’s direction less sensitive to the width of the pencil mark.”
• Three habits that raise a mark without adding knowledge. (1) Answer the command word you were given, not the one you wish you had. If it says “explain”, every sentence needs a reason. (2) Put the unit on every numerical answer and none on a ratio — refractive index has no unit. (3) Give the number of significant figures the data justify: two-figure data cannot support a four-figure answer.
• Core is not a reduced version of Extended. Everything above is examined at full depth on Paper 1 and Paper 3, and every Core statement is examined on Paper 2 and Paper 4 as well. An Extended candidate who skips this page to reach the Supplement summary has skipped roughly two-thirds of the section.
• Supplement extends; it does not replace. Every question above still rests on the Core model beside it — the sine equation only makes sense once you can say which way the ray bends, and regeneration only makes sense once you know what a signal is. Revise each Supplement block immediately after the Core section it belongs to, not as a separate list at the end.
• Two rules that make the gaps work. (1) Always attempt from memory before you look. A failed attempt followed by the answer is worth more than a comfortable re-read, even though it feels worse. (2) Do not shorten the gaps because you feel rusty — feeling rusty is the point at which the recall is doing its work. If a session is missed, carry on from where you are rather than restarting.