Waves

• 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.
• 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.
• Section 3.2.2 in one line. Slower medium, bend towards the normal; faster medium, bend away; \(n = \sin i / \sin r\) with \(i\) in air; \(\sin c = 1/n\); and total internal reflection needs high-\(n\) to low-\(n\) and \(i > c\).
• 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.
• Section 3.2.3 in one line. Two of the three standard rays locate any image; real rays crossing give a real, inverted image; backward extensions crossing give a virtual, upright image; magnification is image length over object length; short sight takes a diverging lens and long sight a converging one.
• 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.
• One order, two readings. Radio · Microwave · Infrared · Visible · Ultraviolet · X-ray · Gamma. Left to right, the frequency rises and the wavelength falls. Whichever quantity a question names, you only need the one list.

• I know that waves transfer energy without transferring matter. 3.1.1
• I can describe wave motion using vibrations in ropes and springs and using water-wave experiments. 3.1.2
• I can describe the features of a wave in terms of wavefront, wavelength, frequency, crest (peak), trough, amplitude and wave speed. 3.1.3
• I can define frequency, wavelength and amplitude precisely. 3.1.4
• I can recall and use \(v = f\lambda\). 3.1.5
• I know that a transverse wave vibrates at right angles to the energy transfer, and I can give examples including electromagnetic radiation, water-surface waves and seismic S-waves. 3.1.6
• I know that a longitudinal wave vibrates parallel to the energy transfer, and I can give examples including sound waves and seismic P-waves. 3.1.7
• I can describe reflection at a plane surface, refraction due to a change of speed, and diffraction through a gap. 3.1.8
• I can describe how wavelength and gap size affect diffraction through a gap. 3.1.9
• I can describe how a ripple tank shows reflection, refraction caused by a depth change, diffraction at a gap and diffraction at an edge. 3.1.10
• I can describe how wavelength affects diffraction at an edge. 3.1.11
• I can define and use the terms normal, angle of incidence and angle of reflection. 3.2.1.1
• I can describe an experiment to illustrate the law of reflection. 3.2.1.2
• I can describe an experiment to find the position and characteristics of the image formed by a plane mirror. 3.2.1.3
• I can state that the angle of incidence equals the angle of reflection and use this in constructions, measurements and calculations. 3.2.1.4
• I can define and use the terms normal, angle of incidence and angle of refraction. 3.2.2.1
• I can define refractive index as \(n = \dfrac{\sin i}{\sin r}\) and recall and use the equation. 3.2.2.2
• I can describe an experiment to show refraction of light by transparent blocks of different shapes. 3.2.2.3
• I can define critical angle and total internal reflection, and recall and use \(n = \dfrac{1}{\sin c}\). 3.2.2.4
• I can describe experiments to show internal reflection and total internal reflection. 3.2.2.5
• I can describe the use of optical fibres, particularly in telecommunications, and state the advantages in each context. 3.2.2.6
• I can describe the action of thin converging and thin diverging lenses on a parallel beam of light. 3.2.3.1
• I can define and use focal length, principal axis and principal focus (focal point). 3.2.3.2
• I can draw ray diagrams for real and virtual images formed by a converging lens, and I know that a real image is formed by converging rays and a virtual image by diverging rays. 3.2.3.3
• I can define linear magnification as the ratio of image length to object length and use the equation. 3.2.3.4
• I can describe the use of a single lens as a magnifying glass. 3.2.3.5
• I can draw ray diagrams showing image formation in the normal eye, the short-sighted eye and the long-sighted eye. 3.2.3.6
• I can describe the use of converging and diverging lenses to correct long-sightedness and short-sightedness. 3.2.3.7
• I can describe dispersion as illustrated by the refraction of white light by a glass prism. 3.2.4.1
• I know the traditional seven colours of the visible spectrum in order of frequency and in order of wavelength. 3.2.4.2
• I know the main regions of the electromagnetic spectrum in order of frequency and in order of wavelength. 3.3.1
• I know that all electromagnetic waves travel at \(3.0 \times 10^{8}\) m/s in a vacuum and at approximately the same speed in air. 3.3.2
• I can describe the role of each region in its stated applications, from radio waves to gamma rays. 3.3.3
• I can describe the damage caused by electromagnetic radiation, including heating of soft tissues and burns, and the ionising effects of ultraviolet, X-rays and gamma rays. 3.3.4
• I can describe the production of sound by vibrating sources. 3.4.1
• I can describe the longitudinal nature of sound waves, including compressions and rarefactions. 3.4.2
• I can state the approximate audible range as 20 Hz to 20 000 Hz. 3.4.3
• I can explain why sound cannot travel in a vacuum and describe an experiment demonstrating this. 3.4.4
• I can describe how changes in amplitude and frequency affect loudness and pitch. 3.4.5
• I can describe how different sources give different sound qualities (timbres), shown by the shape of oscilloscope traces. 3.4.6
• I can describe an echo as the reflection of sound waves. 3.4.7
• I can describe simple experiments showing the reflection of sound waves. 3.4.8
• I can describe a distance-and-time method for determining the speed of sound in air. 3.4.9
• I know that the speed of sound in air is approximately 330–350 m/s. 3.4.10
• I know that sound generally travels faster in solids than in liquids, and faster in liquids than in gases. 3.4.11
• I can define ultrasound as sound with a frequency higher than 20 kHz. 3.4.12
• I can describe uses of ultrasound in cleaning, prenatal and other medical scanning, and sonar, including calculating depth or distance from time and wave speed. 3.4.13

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.

Frequency

Frequency is the number of wavelengths that pass a point per unit time; symbol f, unit hertz, where one hertz is one wave per second. Frequency is fixed by the source and does not change when a wave crosses a boundary.

Reflection

Reflection is the change in direction of a wave when it bounces back from a boundary or plane surface; the wavelength, frequency and speed are unchanged.

Amplitude

Amplitude is the maximum distance a point on the wave moves from its mean (equilibrium) position; it is measured from the middle to a crest, not from crest to trough.

Longitudinal Wave

A longitudinal wave is one in which the direction of vibration is parallel to the direction of energy transfer, producing regions of compression and rarefaction; examples include sound waves and seismic P-waves.

Transverse Wave

A transverse wave is one in which the direction of vibration is at right angles to the direction of energy transfer; examples include electromagnetic radiation, water-surface waves and seismic S-waves.

Wavefront

A wavefront is a line or surface joining points of a wave that are all in phase, such as a line of crests; wavefronts are drawn perpendicular to the direction of travel and one wavelength apart.

Diffraction

Diffraction is the spreading of a wave as it passes through a gap or travels past an edge; it becomes more noticeable when the wavelength is comparable to the size of the gap or obstacle.

Critical Angle

The critical angle is the angle of incidence, measured in the optically denser medium, for which the angle of refraction in the less dense medium is ninety degrees, so the refracted ray travels along the boundary.

Principal Focus

The principal focus of a converging lens is the point on the principal axis to which a beam of light parallel to that axis converges after passing through the lens; for a diverging lens it is the point from which such a beam appears to diverge.

Wavelength

Wavelength is the distance between two consecutive identical points on a wave, such as two consecutive crests; its symbol is lambda and its SI unit is the metre.

Dispersion of light

The separation of white light into the colours of the visible spectrum, which happens because the refractive index of a medium such as glass is slightly different for each frequency. Violet light is slowed most, so it has the largest refractive index and is deviated most; red is deviated least. A prism does not create the colours, it separates colours already present in the white light. In order of increasing frequency the traditional seven colours run red, orange, yellow, green, blue, indigo, violet, and in order of increasing wavelength that order is reversed.

Law of reflection

The normal is the line drawn at right angles to a reflecting surface at the point where a ray strikes it; the angle of incidence is the angle between the incident ray and the normal, and the angle of reflection is the angle between the reflected ray and the normal. The law of reflection states that the angle of incidence equals the angle of reflection, and that the incident ray, the reflected ray and the normal all lie in the same plane.

Electromagnetic Spectrum

The electromagnetic spectrum is the continuous family of transverse waves that all travel at three times ten to the eight metres per second in a vacuum and need no medium, arranged in order of frequency as radio, microwave, infrared, visible, ultraviolet, X-ray and gamma.

Refraction

Refraction is the change in direction of a wave caused by a change in its speed when it passes from one medium into another; frequency stays the same while speed and wavelength both change.

Total Internal Reflection

Total internal reflection is the complete reflection of light back into the denser medium at a boundary; it occurs only when light travels from a medium of higher refractive index to one of lower refractive index and the angle of incidence is greater than the critical angle.

Sound

Sound is a longitudinal mechanical wave produced by a vibrating source, consisting of compressions and rarefactions travelling through a material medium; it cannot travel through a vacuum.

Ultrasound

Ultrasound is sound with a frequency higher than 20 kHz, above the upper limit of human hearing; it is used in cleaning, in prenatal and other medical scanning, and in sonar for measuring depth and distance.

Refractive Index

Refractive index n is defined as the ratio of the sine of the angle of incidence to the sine of the angle of refraction for light passing from air into the medium; it has no unit and is greater than one for transparent solids and liquids.

Focal Length

Focal length is the distance from the optical centre of a lens to its principal focus; a more powerful lens has a shorter focal length.

• 1. “Waves transport particles from the source to the receiver.” 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.” 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.” 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.” 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.” 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.” 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.” Why wrongEvery optical law in this topic — \(i = r\), \(n = \sin i / \sin r\), \(n = 1/\sin c\) — is defined with respect to the normal. 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.” 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.” 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.” 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.” 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.” 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.” 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.” 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.” 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.” Why wrongA radio wave is transverse, electromagnetic, travels at \(3.0 \times 10^{8}\) m/s 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.” 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 \(3.0 \times 10^{8}\) m/s. Say this“Electromagnetic waves do not require a material medium and travel through a vacuum at \(3.0 \times 10^{8}\) m/s.” CheckAstronauts on a spacewalk can see each other but must use radios to talk. Explain both facts.
• 18. “All electromagnetic waves are equally dangerous.” 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 is linked to skin cancer and cataracts, X-rays and gamma rays to cell mutation and cancer. 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.” 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.” 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 an oscilloscope trace tells you the loudness?
• 21. “Sound travels fastest in gases.” 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.” 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 \(vt\).” 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.)

• How to use this list. 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. Practise them in that form, not as continuous prose.
• 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 energy transfer; in a longitudinal wave the vibration is parallel to it.”
• 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.
• 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.”
• 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.
• 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 and magnification have no units. (3) Give the number of significant figures the data justify: two-figure data cannot support a four-figure answer.