C.2 Wave model flashcards: IB Physics SL and HL

All 69 C.2 Wave model cards

1. DefinitionSL & HL

   Define a progressive (travelling) wave and state precisely what is and is not transferred by it.

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   A progressive wave is a disturbance that travels through space or a medium, transferring energy (and momentum) from one point to another without any net transfer of matter. The particles of the medium oscillate about fixed equilibrium positions; each particle sets the next one moving, so the disturbance advances while the matter does not. Exam tip: the mark is for "energy transfer without net transfer of matter" — omitting the word net loses it, because particles do move locally. Do not say a wave "carries particles"; a cork on water bobs but stays put. Wave speed is a property of the medium, not of the source.

2. DefinitionSL & HL

   Define a transverse wave and give two examples.

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   A transverse wave is one in which the oscillations (displacements) of the particles or fields are perpendicular to the direction of energy transfer / wave propagation. Examples: waves on a stretched string, water surface ripples, and all electromagnetic waves (oscillating electric and magnetic fields perpendicular to each other and to the direction of travel). Exam tip: the mark requires "perpendicular to the direction of energy transfer (or propagation)" — "perpendicular to the wave" is too vague. Transverse mechanical waves cannot travel through the body of a gas or liquid because fluids cannot sustain shear, which is why S-waves do not pass through Earth's liquid outer core.

3. DefinitionSL & HL

   Define a longitudinal wave and give two examples.

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   A longitudinal wave is one in which the oscillations of the particles are parallel to (along) the direction of energy transfer / wave propagation. Examples: sound in air, solids or liquids, and P-waves in seismology; a slinky pushed and pulled along its length. Exam tip: state parallel to the direction of energy transfer, not merely "in the same direction as the wave". Longitudinal waves need a material medium, so sound cannot travel through a vacuum. They travel as a series of compressions (regions of higher pressure and density) and rarefactions (lower pressure and density) that move at the wave speed.

4. DefinitionSL & HL

   Define crest, trough, compression and rarefaction, and state the separation of adjacent equivalents in each case.

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   Crest: a point of maximum positive displacement on a transverse wave. Trough: maximum negative displacement. Compression: a region of a longitudinal wave where particles are closest together, so density and pressure are maximum. Rarefaction: a region where particles are furthest apart, so density and pressure are minimum. Adjacent crests, adjacent troughs, adjacent compressions or adjacent rarefactions are separated by exactly one wavelength λ; a crest and the next trough (or a compression and the next rarefaction) are separated by λ/2. Exam tip: at the centre of a compression the particle displacement is zero, not maximum — displacement and pressure are a quarter-cycle out of step.

5. DefinitionSL & HL

   Define displacement and amplitude for a wave, and state their units and vector/scalar nature.

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   Displacement x (or y) is the distance and direction of a particle from its equilibrium (undisturbed) position at a given instant; it is a vector, unit metre (m), and it varies continuously between +A and −A. Amplitude A is the maximum magnitude of the displacement from equilibrium; it is a scalar (a magnitude only), unit metre. For sound, amplitude may instead be quoted as a maximum pressure variation in Pa. Exam tip: amplitude is measured from the equilibrium line to a crest, not from trough to crest — halving that peak-to-peak height is the classic slip. Intensity is proportional to A², so doubling amplitude quadruples the energy delivered per second.

6. DefinitionSL & HL

   Define wavelength and state how it is identified on both types of wave.

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   Wavelength λ is the shortest distance along the direction of propagation between two points on the wave that are oscillating in phase — for example, crest to adjacent crest, trough to adjacent trough, or compression to adjacent compression. Unit metre (m); it is a scalar. Exam tip: the safe mark-scheme wording is "distance between two consecutive points in phase"; "distance between two crests" without consecutive/adjacent is often not credited. On a displacement–distance graph λ is read off the x-axis; on a displacement–time graph you cannot read λ at all, only the period T.

7. DefinitionSL & HL

   Define the period of a wave and state its unit.

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   The period T is the time taken for one complete oscillation of a particle of the medium, equivalently the time for one whole wavelength to pass a fixed point. Unit second (s); scalar. It is the reciprocal of frequency, T = 1/f. Exam tip: define period in terms of one complete cycle — "time for the wave to move" scores nothing. Read T from a displacement–time graph as the horizontal distance between successive identical points (e.g. crest to crest, or every second zero-crossing in the same direction); reading only to the next zero gives T/2 and is a very common error.

8. DefinitionSL & HL

   Define the frequency of a wave and state its unit.

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   Frequency f is the number of complete oscillations (cycles) per unit time made by a particle of the medium, equivalently the number of whole wavelengths passing a fixed point per second. Unit hertz (Hz), where 1 Hz = 1 s⁻¹; scalar. Exam tip: the frequency of a wave is set by the source and does not change when the wave enters a new medium — only λ and v change. Quoting "waves per second" is acceptable but "oscillations per second" is safer. Audible sound spans about 20 Hz to 20 kHz; visible light is about 4.3 × 10¹⁴ to 7.5 × 10¹⁴ Hz.

9. DefinitionSL & HL

   Define wave speed and state what it depends on.

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   Wave speed v (c for electromagnetic waves) is the distance travelled per unit time by a point of constant phase, such as a crest or a wavefront; unit m s⁻¹, and it is the speed of energy transfer through the medium. It is determined by the properties of the medium (tension and mass per unit length for a string; temperature, and hence stiffness and density, for a gas), not by the frequency or amplitude of the source. Exam tip: do not confuse the wave speed with the oscillation speed of a particle, which varies from zero at the extremes to a maximum at zero displacement and is usually far smaller.

10. DefinitionSL & HLData booklet: No – derive

    Define the intensity of a wave and state its unit.

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    Intensity I is the power transferred by the wave per unit area at right angles to the direction of propagation: I = P/A. Unit W m⁻² (equivalently J s⁻¹ m⁻²); it is a scalar. For a given wave, intensity is proportional to the square of the amplitude, I ∝ A², and for a point source radiating uniformly into space it obeys the inverse-square law I ∝ x⁻². Exam tip: the area must be perpendicular to the propagation direction; if a surface is tilted, the intercepted power falls. Intensity is an average over many cycles, so it is not the instantaneous energy at a crest. Note the booklet prints only the proportionalities I ∝ A² and I ∝ x⁻²; I = P/A itself must be derived.

11. DefinitionSL & HLData booklet: No – memorise

    Define phase difference and state the values for points in phase and in antiphase.

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    Phase difference is the fraction of a cycle by which one oscillation leads or lags another, expressed as an angle in radians (0 to 2π) or degrees (0° to 360°). Two points are in phase when the phase difference is 0 or a whole multiple of 2π (360°), which happens when their separation is a whole number of wavelengths; they are in antiphase when it is π rad (180°), i.e. separation is an odd number of half-wavelengths. Exam tip: quote phase difference with a unit (rad or °), never as a bare number, and remember that in-phase points have the same displacement and the same direction of motion — equal displacement alone is not enough.

12. DefinitionSL & HL

    Define a wavefront and a ray, and state the relationship between them.

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    A wavefront is a surface (a line in two dimensions) joining adjacent points of a wave that are oscillating in phase — for example the line along successive crests; consecutive wavefronts are one wavelength apart. A ray is a line drawn with an arrow showing the direction in which the wave energy travels. Rays are always perpendicular (normal) to the wavefronts. Exam tip: a point source gives circular/spherical wavefronts with radial rays; far from the source the wavefronts are effectively plane and the rays parallel. Marks are lost for drawing rays at an angle to wavefronts, for unequal wavefront spacing in a uniform medium, and for omitting the arrowhead on a ray.

13. DefinitionSL & HL

    Describe sound as a longitudinal wave and state its key numerical properties in air.

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    Sound is a longitudinal mechanical wave: a vibrating source pushes the air, producing travelling compressions (pressure and density above ambient) and rarefactions (below ambient); each air molecule oscillates parallel to the propagation direction about a fixed position. It requires a medium, so it cannot travel through a vacuum. Speed in air ≈ 340 m s⁻¹ at room temperature (rising with temperature), ≈ 1500 m s⁻¹ in water and ≈ 5000 m s⁻¹ in steel. The audible range for humans is about 20 Hz to 20 kHz. Exam tip: loudness relates to amplitude (and hence intensity), pitch to frequency — swapping these is a routine lost mark.

14. DefinitionSL & HL

    State what physically oscillates in a wave on a string, in a sound wave and in an electromagnetic wave, and why one wave model describes all three.

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    String wave: the transverse displacement of the string material about its equilibrium line. Sound: the longitudinal displacement of the particles of the medium, seen macroscopically as a variation of pressure and density about ambient values. Electromagnetic wave: the electric and magnetic field strengths, oscillating perpendicular to each other and to the direction of travel — nothing material moves. The single wave model applies because all three are described by the same quantities (λ, f, T, v, A, intensity) and obey v = fλ and T = 1/f. Exam tip: Nature of Science — this is a powerful unifying model, and Maxwell's prediction that light is an EM wave travelling at c was confirmed by Hertz.

15. EquationSL & HLData booklet: Yes

    State the wave equation, define every symbol with its unit and give its conditions of validity.

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    c = fλ (data booklet), usually written v = fλ for mechanical waves. v (or c) = wave speed in m s⁻¹; f = frequency in Hz (s⁻¹); λ = wavelength in m. Valid for any progressive wave in any medium, and follows directly from speed = distance/time with distance λ in time T: v = λ/T = fλ. Conditions: v must be the speed in the medium the wavelength is measured in. Common misuse: when a wave crosses into a new medium students change f; f is fixed by the source, so if v falls, λ falls in the same ratio. Sanity check: 340 = f × 0.68 m gives f = 500 Hz, an audible mid-range tone.

16. EquationSL & HLData booklet: Yes

    State the relationship between period and frequency and define the symbols.

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    T = 1/f (data booklet), equivalently f = 1/T. T = period in seconds (s); f = frequency in hertz (Hz = s⁻¹). Valid for any periodic oscillation or wave, whatever its shape. Rearranged forms you must know: f = 1/T, and for n complete cycles in time t, T = t/n and f = n/t. Common misuse: mixing prefixes — for f = 50 MHz, T = 1/(50 × 10⁶) = 2.0 × 10⁻⁸ s = 20 ns, not 0.02 s. Sanity check: mains at 50 Hz gives T = 0.020 s; a 440 Hz tuning fork gives T = 2.27 × 10⁻³ s. Timing many oscillations and dividing by n reduces the fractional uncertainty in T.

17. EquationSL & HLData booklet: No – derive

    State the form of the wave equation that uses the period, and show how it follows.

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    v = λ/T. v = wave speed in m s⁻¹; λ = wavelength in m; T = period in s. It comes from speed = distance/time: in exactly one period the wave profile advances exactly one wavelength. Substituting T = 1/f recovers the booklet form c = fλ. Not printed separately in the booklet — derive it. Use it whenever a displacement–time graph gives T and a displacement–distance graph gives λ for the same wave, since neither graph alone gives v. Common misuse: taking λ and T from graphs of two different waves. Sanity check: λ = 2.0 m with T = 0.50 s gives v = 4.0 m s⁻¹.

18. EquationSL & HLData booklet: No – derive

    State the defining equation for intensity and define each symbol with units.

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    I = P/A. I = intensity in W m⁻²; P = power (rate of energy transfer) of the wave in watts (W = J s⁻¹); A = area in m², measured perpendicular to the direction of propagation. Equivalently I = E/(At) with E the energy in joules and t the time in seconds. Valid for any wave carrying energy through a surface. Common misuse: using the area of a tilted surface without resolving, or using the source's total surface area rather than the area at the detector. Sanity check: a 60 W lamp assumed 100% efficient at 2.0 m gives I = 60/(4π × 2.0²) = 1.2 W m⁻².

19. EquationSL & HLData booklet: Yes

    State how the intensity of a wave depends on its amplitude and give the ratio form.

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    I ∝ A² (data booklet). I = intensity in W m⁻²; A = amplitude in m (or Pa for sound). Hence I = kA² for a fixed wave in a fixed medium, and the ratio form I₁/I₂ = (A₁/A₂)², rearranged as A₁/A₂ = √(I₁/I₂). Valid for a given wave type in a given medium where no energy is absorbed. Common misuse: writing I ∝ A, so that doubling the amplitude is claimed to double the intensity — it quadruples it, and tripling A gives 9I. Sanity check: to halve the intensity, the amplitude must fall by a factor √2, i.e. to about 71% of its original value.

20. EquationSL & HLData booklet: Yes

    State the inverse-square law for intensity and its conditions of validity.

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    I ∝ x⁻², i.e. I ∝ 1/x² (data booklet), where I = intensity in W m⁻² and x = distance from the source in m. Ratio form: I₁/I₂ = (x₂/x₁)², so I₂ = I₁(x₁/x₂)². Conditions: a point (or small) source radiating uniformly in all directions, no absorption or scattering by the medium, and no reflection or focusing. Common misuse: applying it to a laser beam or a parallel beam, where intensity is essentially constant with distance. Sanity check: tripling the distance reduces the intensity to one ninth; moving from 2.0 m to 6.0 m cuts 45 W m⁻² to 5.0 W m⁻².

21. EquationSL & HLData booklet: No – derive

    Give the combined expression for the intensity at distance r from a point source of power P, and state how it arises.

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    I = P/(4πr²). I = intensity in W m⁻²; P = power emitted by the source in W; r = distance from the source in m. It follows from I = P/A with A = 4πr², the surface area of a sphere of radius r centred on the source, and it combines the booklet relations I = P/A and I ∝ x⁻². Conditions: point source, uniform emission in all directions, no absorption. Common misuse: using 2πr² or πr². Sanity check: a star of luminosity 3.8 × 10²⁶ W seen at 1.5 × 10¹¹ m gives I = 3.8 × 10²⁶/(4π × (1.5 × 10¹¹)²) ≈ 1.3 × 10³ W m⁻², the solar constant.

22. EquationSL & HLData booklet: No – memorise

    State the equation linking phase difference to path difference and define each symbol.

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    Δφ = 2πΔx/λ in radians, or Δφ = 360°(Δx/λ) in degrees. Δφ = phase difference (rad or °); Δx = path difference / separation of the two points along the direction of propagation, in m; λ = wavelength in m. Not in the data booklet — memorise. Valid for two points on the same wave, or two waves of the same frequency travelling in the same medium. Rearranged: Δx = λΔφ/2π. Common misuse: forgetting that only the fractional part matters, so Δx = 2.25λ gives Δφ = 0.25 × 2π = π/2 rad, not 4.5π. Sanity check: Δx = λ/4 gives 90°, λ/2 gives 180° (antiphase).

23. EquationSL & HLData booklet: No – memorise

    State the equation linking phase difference to a time delay between two oscillations.

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    Δφ = 2πΔt/T = 2πfΔt in radians, or Δφ = 360°(Δt/T) in degrees. Δφ = phase difference (rad or °); Δt = time lag between the two oscillations in s; T = period in s; f = frequency in Hz. Not in the booklet — memorise. Use it when a displacement–time graph shows two particles whose motions are shifted horizontally, or when a signal arrives late at a detector. Common misuse: mixing Δt with T from different waves, or using degrees in a calculation set up in radians. Sanity check: Δt = T/8 gives Δφ = π/4 rad = 45°; a lag of one whole period gives 2π rad, i.e. in phase.

24. EquationSL & HLData booklet: No – derive

    State the equation used to find the speed of sound by the echo (timing) method and define the symbols.

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    v = 2d/t. v = speed of sound in m s⁻¹; d = perpendicular distance from the source to the reflecting wall in m; t = total time in s between making the sound and hearing the echo. The factor 2 appears because the sound travels to the wall and back. Not in the booklet — derive from v = distance/time. Common misuse: forgetting the factor 2, which halves the answer to about 170 m s⁻¹ and is instantly recognisable to a marker. Sanity check: d = 85 m and t = 0.50 s give v = 2 × 85/0.50 = 340 m s⁻¹. Repeat and average, and use a large d, to reduce the fractional uncertainty in the human reaction time.

25. EquationSL & HLData booklet: No – derive

    State the ratio relationships that let you compare two positions in the field of a point source without knowing its power.

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    I₁/I₂ = (x₂/x₁)² and A₁/A₂ = √(I₁/I₂) = x₂/x₁. I = intensity in W m⁻²; x = distance from the source in m; A = amplitude in m. These follow from I ∝ x⁻² and I ∝ A², both in the booklet, and they eliminate the unknown source power P. Hence the amplitude of a spherical wave falls as 1/x while the intensity falls as 1/x². Conditions: point source, uniform emission, no absorption. Common misuse: applying the amplitude result with a square, giving 1/x². Sanity check: doubling the distance halves the amplitude but quarters the intensity.

26. EquationSL & HLData booklet: Yes

    State the speed of all electromagnetic waves in a vacuum and show how it fixes the frequency–wavelength trade-off.

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    c = 3.00 × 10⁸ m s⁻¹ for every electromagnetic wave in a vacuum, regardless of frequency or amplitude; c = fλ therefore gives f = c/λ, so f ∝ 1/λ across the whole spectrum. c is in the data booklet as a constant; the relation c = fλ is also printed. Conditions: vacuum (in a medium the speed is lower, so λ shortens while f is unchanged). Common misuse: assuming red light travels more slowly than blue in vacuum — they are identical. Sanity check: λ = 600 nm gives f = 3.00 × 10⁸/(6.00 × 10⁻⁷) = 5.00 × 10¹⁴ Hz; a 100 MHz FM station has λ = 3.00 m.

27. EquationSL & HLData booklet: No – derive

    State how the number of complete waves passing a point relates to time and distance, with symbols defined.

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    Number of cycles n = ft = t/T, and the distance covered by the wave in that time is d = nλ = vt. n = number of complete oscillations (a pure number); f = frequency in Hz; t = time in s; T = period in s; λ = wavelength in m; v = wave speed in m s⁻¹; d = distance in m. Not in the booklet — derive from f = 1/T and v = fλ. Common misuse: counting crests on a graph rather than complete cycles, which typically gives an answer out by one. Sanity check: a 250 Hz sound heard for 2.0 s delivers 500 complete waves and has travelled 500 × 1.36 = 680 m at 340 m s⁻¹.

28. Graph/diagramSL & HL

    Describe the displacement–distance graph of a progressive wave and state everything that can be read from it.

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    Axes: displacement y/m (or cm) on the y-axis against distance x/m along the direction of propagation on the x-axis; the shape is a sinusoid. It is a snapshot of the whole wave at one instant. From it read the wavelength λ (distance between adjacent points in phase, e.g. crest to crest, or twice the distance between adjacent zeros) and the amplitude A (equilibrium line to a crest). You cannot read T or f from it; combine with v = fλ if v is given, or with a displacement–time graph. Changing a parameter: raising f at fixed v compresses the pattern horizontally; increasing the source power stretches it vertically since A ∝ √I.

29. Graph/diagramSL & HL

    Describe the displacement–time graph for one particle in a progressive wave and state what can be extracted from it.

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    Axes: displacement y/m on the y-axis against time t/s on the x-axis; the shape is a sinusoid. It shows the motion of a single particle, not the shape of the wave. From it read the period T (time between adjacent points in phase) and hence f = 1/T, and the amplitude A. The gradient at any point is the particle's velocity: maximum at zero displacement, zero at a crest or trough. You cannot read λ from it. Changing a parameter: doubling f halves the horizontal spacing; damping produces a decaying envelope. Exam tip: axis labels decide which quantity a student is allowed to quote — always check the x-axis unit first.

30. Graph/diagramSL & HL

    Describe the displacement and pressure graphs for a sound wave and state the relationship between them.

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    For a sound wave travelling along x, plot particle displacement/m against distance/m, and separately pressure variation Δp/Pa (deviation from ambient) against distance/m. Both are sinusoidal with the same λ, but they are a quarter of a wavelength (π/2 rad, 90°) out of step: where displacement is zero and particles converge, pressure is a maximum (centre of a compression); where displacement is zero and particles diverge, pressure is a minimum (centre of a rarefaction); at points of maximum displacement the pressure equals the ambient value. The pressure amplitude is proportional to the displacement amplitude, so intensity ∝ (Δp_max)². Changing a parameter: louder sound raises both amplitudes; higher pitch compresses both graphs horizontally.

31. Graph/diagramSL & HL

    Describe the graph of intensity against distance from a point source and the linearisation used in IB practicals.

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    Axes: intensity I/W m⁻² (y) against distance x/m (x). The shape is a steeply falling curve of decreasing gradient, asymptotic to both axes — a rectangular hyperbola-like inverse-square decay, never a straight line and never touching the x-axis. To verify the law, linearise: plot I against 1/x² (units m⁻²), which gives a straight line through the origin of gradient P/4π, so the source power is P = 4π × gradient. Alternatively plot ln I against ln x: a straight line of gradient −2 confirms the inverse-square law. Changing a parameter: doubling the source power doubles the gradient but leaves the shape and the −2 log gradient unchanged.

32. Graph/diagramSL & HL

    Describe the graph of intensity against amplitude and how it is linearised.

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    Axes: intensity I/W m⁻² (y) against amplitude A/m (x). Since I ∝ A², the shape is a parabola through the origin with increasing gradient. Linearise by plotting I against A² (units m²): a straight line through the origin whose gradient is the constant of proportionality k in I = kA², from which the intensity at any other amplitude follows. A log–log plot of ln I against ln A gives a straight line of gradient 2 and is the usual way to test the exponent experimentally. Changing a parameter: absorbing medium or an inefficient detector lowers the gradient but keeps the line straight and through the origin; a non-zero intercept signals background intensity not subtracted.

33. Graph/diagramSL & HL

    Describe how wavefront and ray diagrams are drawn for plane and circular waves, and what the spacing represents.

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    Wavefronts are drawn as lines joining points in phase (usually successive crests) separated by exactly one wavelength; rays are arrowed lines perpendicular to them showing the direction of energy transfer. A point source gives concentric circular (spherical) wavefronts with radial rays; a straight dipper or a distant source gives parallel straight wavefronts with parallel rays. The spacing of the wavefronts is λ, so a change of spacing signals a change of wave speed: entering a slower medium at normal incidence, the wavefronts bunch closer together while their frequency is unchanged. Exam tip: keep the spacing uniform within one medium and always draw rays at 90° to the fronts, with arrowheads.

34. Graph/diagramSL & HL

    Describe the graph used to determine the speed of sound from a resonance-tube or standing-wave experiment by plotting wavelength against 1/f.

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    Axes: wavelength λ/m (y) against 1/f (s, i.e. Hz⁻¹) on the x-axis, obtained by finding the resonant length for each of several tuning-fork frequencies. Since λ = v/f = v(1/f), the graph is a straight line through the origin with gradient equal to the speed of sound v in m s⁻¹. Draw maximum and minimum gradient lines through the error bars to quote v with an uncertainty. If λ is taken as 4L from the measured resonant length L, the line has a small negative y-intercept of −4e, revealing the end correction e, since the antinode lies slightly beyond the open end so L is always less than λ/4. Changing a parameter: raising the air temperature increases v and so steepens the line without changing the intercept.

35. Concept/explainSL & HL

    Explain the difference between a transverse and a longitudinal wave, and state how each type is identified from a diagram or a demonstration.

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    • In a transverse wave the oscillation of the medium (or field) is perpendicular to the direction of energy transfer/propagation
    • In a longitudinal wave the oscillation is parallel to the direction of energy transfer
    • Transverse waves show crests and troughs; longitudinal waves show compressions (regions of high pressure/density) and rarefactions (low pressure/density)
    • Examples: waves on a string, water surface waves and all electromagnetic waves are transverse; sound in air and P-waves are longitudinal
    • Both transfer energy without net transfer of matter
    • On a slinky, a sideways flick gives a transverse pulse, a push-pull along the axis gives a longitudinal pulse. Exam tip: students lose the mark by writing "the wave moves up and down" — you must compare the direction of oscillation with the direction of propagation.
36. Concept/explainSL & HL

    Distinguish between mechanical and electromagnetic waves.

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    • A mechanical wave is a propagating disturbance of a material medium; particles of the medium oscillate about fixed equilibrium positions
    • Mechanical waves therefore require a medium and cannot travel through a vacuum
    • Their speed is fixed by properties of the medium (elasticity/tension and density/inertia), so sound travels faster in solids than in gases
    • An electromagnetic wave is a propagating oscillation of electric and magnetic fields, mutually perpendicular and perpendicular to the direction of travel
    • EM waves need no medium and travel at c = 3.00 × 10⁸ m s⁻¹ in a vacuum, whatever their frequency
    • All EM waves are transverse; mechanical waves may be transverse or longitudinal. Exam tip: a bell in an evacuated jar is the standard evidence — the light still gets out, the sound does not.
37. Concept/explainSL & HL

    Explain what is meant by the statement that a travelling (progressive) wave transfers energy without a net transfer of matter.

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    • A progressive wave is a disturbance that propagates through space, carrying energy and momentum away from the source
    • Each particle of the medium oscillates about a fixed equilibrium position and returns to it every period
    • Neighbouring particles are set into oscillation slightly later, so the pattern of disturbance advances even though no particle advances with it
    • The energy is carried as the kinetic energy of the oscillating particles plus the potential energy stored in the deformation of the medium
    • Evidence: a cork on water bobs up and down as ripples pass but does not drift across the tank; dust in front of a loudspeaker vibrates in place
    • Energy per unit time per unit area is the intensity. Exam tip: the commonest error is claiming that the water (or air) itself travels from source to receiver.
38. Concept/explainSL & HL

    Explain what happens to the speed, frequency and wavelength of a wave when it passes from one medium into another.

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    • The frequency is determined by the source and is unchanged on crossing a boundary — the oscillations at the boundary drive the second medium at the same rate
    • If frequency changed, oscillations would have to be created or destroyed at the boundary, which is impossible
    • The wave speed is a property of the medium (its elasticity/stiffness and density, or its refractive index for light) so it changes at the boundary
    • Since c = fλ with f constant, wavelength changes in the same proportion as the speed: slower medium → shorter wavelength
    • For light entering glass, v and λ fall by a factor n; the colour (frequency) is unchanged
    • The change in speed is what produces refraction. Exam tip: a common error is to state that light "slows down so its frequency drops" — this scores zero.
39. Concept/explainSL & HL

    Explain what is meant by the phase difference between two points on a progressive wave, and how it is related to their separation.

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    • Two points oscillate with the same period; the phase difference measures how far one lags behind the other within a cycle
    • It is expressed as a fraction of a cycle, in degrees, or in radians: Δφ = 2πΔx/λ (equivalently 360° × Δx/λ)
    • Points separated by a whole number of wavelengths are in phase (Δφ = 0, 2π, 4π …): they have the same displacement and velocity at all times
    • Points separated by an odd number of half-wavelengths are in antiphase (Δφ = π): equal and opposite displacements
    • Phase difference can also be read from displacement–time graphs as a time lag Δt, with Δφ = 2πΔt/T
    • Path difference and phase difference are the same idea in different units. Exam tip: state the unit (rad or °) and do not confuse a phase difference with a path difference in metres.
40. Concept/explainSL & HL

    Outline how sound propagates through air as a longitudinal wave, and describe the relationship between the displacement graph and the pressure graph.

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    • A vibrating source (loudspeaker cone, tuning fork prong) pushes air molecules together, creating a compression — a region of above-average pressure and density
    • As the source moves back it leaves a rarefaction — below-average pressure and density
    • These regions travel outwards; individual molecules oscillate parallel to the propagation direction about fixed positions
    • Wavelength is the distance between adjacent compressions (or adjacent rarefactions)
    • At a compression or rarefaction the displacement of the molecules is zero but the pressure change is maximum; where displacement is maximum the pressure change is zero
    • Hence the pressure variation is 90° (π/2) out of phase with the displacement variation. Exam tip: students routinely draw the pressure and displacement curves in phase — the quarter-cycle shift is the marking point.
41. Concept/explainSL & HL

    Outline the electromagnetic spectrum: the order of the regions and the properties all electromagnetic waves share.

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    • In order of increasing wavelength (decreasing frequency): gamma rays, X-rays, ultraviolet, visible, infrared, microwaves, radio waves
    • Approximate wavelengths: gamma < 10⁻¹² m, X-ray 10⁻¹²–10⁻⁸ m, UV 10⁻⁸–4 × 10⁻⁷ m, visible 4 × 10⁻⁷–7 × 10⁻⁷ m (violet → red), IR 7 × 10⁻⁷–10⁻³ m, microwave 10⁻³–10⁻¹ m, radio > 10⁻¹ m
    • All are transverse oscillations of perpendicular electric and magnetic fields
    • All travel at c = 3.00 × 10⁸ m s⁻¹ in a vacuum, so c = fλ links every region
    • None requires a medium; all can be reflected, refracted, diffracted and superposed
    • Real-world: the same wave model describes a radio broadcast and a medical X-ray. Exam tip: learn the order and at least one order-of-magnitude wavelength per region — "about 500 nm for visible" is the anchor.
42. Concept/explainSL & HL

    Explain why the intensity of a wave is proportional to the square of its amplitude.

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    • Intensity is the power transferred per unit area perpendicular to the direction of propagation, in W m⁻²
    • The energy carried by a wave is the energy of the oscillating particles (or fields) it sets into motion
    • For simple harmonic oscillation the total energy of an oscillator is proportional to the square of its amplitude, since E = ½kA²
    • Therefore the energy delivered per second through unit area, i.e. the intensity, is also proportional to A²: I ∝ A² (data booklet)
    • Consequences: doubling the amplitude quadruples the intensity; halving the intensity reduces amplitude by a factor √2
    • Combined with I ∝ x⁻² for a point source, A ∝ 1/x for a spherical wave. Exam tip: incomplete answers write I ∝ A; the square comes from the energy of an oscillator, not from the wave equation.
43. Concept/explainSL & HL

    Explain why the intensity of radiation from a point source falls off as the inverse square of the distance, and state the assumptions made.

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    • A point source emits power P uniformly in all directions
    • At distance x the energy has spread over the surface of a sphere of area 4πx², so I = P/(4πx²) and hence I ∝ x⁻² (data booklet)
    • Trebling the distance reduces the intensity to one ninth; since I ∝ A², the amplitude falls as 1/x
    • Assumptions: the source is small compared with x (effectively a point), it radiates isotropically, and no energy is absorbed or scattered between source and detector
    • Real-world: apparent brightness of stars, b = L/(4πd²), and the safe-distance rules for gamma sources both use this law
    • A laser beam does not obey it because the beam is collimated, not spherical. Exam tip: quote the assumption of no absorption — it is a frequent "suggest" mark.
44. Concept/explainSL & HL

    Explain what quantities can be read from a displacement–distance graph and from a displacement–time graph of the same wave.

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    • A displacement–distance graph is a "snapshot" of the whole wave at one instant: the x-axis is position in m
    • From it read the amplitude (maximum displacement from equilibrium) and the wavelength λ (distance between successive points in phase)
    • It also shows the relative phase of different points at that moment
    • A displacement–time graph follows one single particle: the x-axis is time in s
    • From it read the amplitude and the period T (time for one complete oscillation), and hence f = 1/T
    • Neither graph alone gives the wave speed: combine them with c = fλ
    • The two curves can look identical, so the axis label and unit are decisive
    • For a longitudinal wave, positive displacement is conventionally taken along the direction of propagation. Exam tip: always check the x-axis unit before calling a length "the wavelength".
45. Concept/explainSL & HL

    Explain why sound travels faster in solids than in gases, and how the speed of sound in air depends on temperature.

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    • Wave speed in a medium depends on a restoring (elastic) property and an inertial (density) property; qualitatively v increases with stiffness and decreases with inertia per particle
    • In a solid the interparticle bonds are strong and the particles closely spaced, so a disturbance is passed on almost immediately; speeds are of order 5000 m s⁻¹ in steel
    • In a gas the particles are far apart and interact only during collisions, so transmission is much slower, about 340 m s⁻¹ in air
    • Raising the temperature of a gas increases the mean molecular speed, so momentum and energy are passed between molecules more rapidly and the speed of sound rises (roughly ∝ √T in kelvin)
    • Speed of sound in air is essentially independent of pressure and of the frequency or loudness of the sound. Exam tip: do not claim a louder or higher-pitched sound travels faster.
46. Concept/explainSL & HL

    Explain why electromagnetic waves can travel through a vacuum but sound cannot.

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    • Sound is a mechanical wave: it propagates by particles of a medium colliding with and displacing their neighbours
    • A vacuum contains no particles, so there is nothing to compress or rarefy and no mechanism to pass the disturbance on
    • An electromagnetic wave is a self-sustaining oscillation of electric and magnetic fields: a changing electric field generates a changing magnetic field and vice versa
    • These fields exist in empty space, so no material medium is needed
    • The demonstration is an electric bell inside a bell jar: as the air is pumped out the sound fades to nothing while the bell is still clearly seen to be ringing
    • Nature of science: this evidence forced the abandonment of the "luminiferous ether" model for light. Exam tip: "there are no particles in a vacuum" alone is not enough — say what the particles were needed for.
47. Concept/explainSL & HL

    Explain how frequency, period, wavelength and wave speed are related, and state what determines each.

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    • The period T is the time for one complete oscillation of a particle; the frequency f = 1/T is the number of oscillations per second, in Hz (s⁻¹)
    • The frequency of a wave is fixed by the source and does not change as the wave travels or crosses a boundary
    • The wave speed c is fixed by the medium (and, for EM waves in vacuum, is the universal constant c)
    • The wavelength λ is the distance travelled by the wave in one period, so λ = cT = c/f, giving c = fλ (data booklet)
    • Hence for a fixed medium, f and λ are inversely proportional
    • Amplitude is independent of all of these; changing loudness or brightness does not change f, λ or c. Exam tip: students often say "a higher frequency wave travels faster" — in a given medium the speed is the same for all frequencies.
48. Worked problemSL & HLData booklet: Yes

    A radio station broadcasts at 96.0 MHz. Determine the wavelength of the radio wave in air.

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    Principle: for an electromagnetic wave in air, c = fλ with c = 3.00 × 10⁸ m s⁻¹ (data booklet). Rearrange: λ = c/f. Substitute: λ = (3.00 × 10⁸ m s⁻¹)/(96.0 × 10⁶ Hz). Intermediate: 3.00 × 10⁸/9.60 × 10⁷ = 3.125 m. Answer: λ = 3.13 m (3 s.f.). Check/Trap: convert MHz to Hz (× 10⁶) before dividing — the single commonest slip here is an answer of 3.13 × 10⁶ m or 3.13 × 10⁻⁶ m; a sanity check is that FM radio wavelengths are a few metres, which is why FM aerials are about a metre long.

49. Worked problemSL & HLData booklet: Yes

    A tuning fork of frequency 512 Hz is sounded in air, where the speed of sound is 340 m s⁻¹. Calculate the wavelength and the period of the sound wave.

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    Principle: c = fλ (data booklet) and T = 1/f (data booklet). Wavelength: λ = c/f = (340 m s⁻¹)/(512 Hz) = 0.6640… m = 0.664 m (3 s.f.). Period: T = 1/f = 1/512 Hz = 1.953 × 10⁻³ s = 1.95 × 10⁻³ s (3 s.f.). Check/Trap: the wavelength of audible sound is of order tens of centimetres to metres, so 0.66 m is reasonable; do not use c = 3.00 × 10⁸ m s⁻¹ for sound. Note also that if the same fork is sounded in water (v ≈ 1500 m s⁻¹) the frequency stays 512 Hz and the wavelength rises to about 2.9 m.

50. Worked problemSL & HLData booklet: Yes

    A displacement–time graph for one particle in a wave shows a complete oscillation taking 0.40 s and a maximum displacement of 6.0 mm. A displacement–distance graph of the same wave gives a wavelength of 1.5 m. Determine the frequency, the amplitude and the speed of the wave.

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    Principle: read T and A from the displacement–time graph, λ from the displacement–distance graph, then use f = 1/T and c = fλ (both data booklet). Frequency: f = 1/T = 1/0.40 s = 2.5 Hz. Amplitude: A = 6.0 mm = 6.0 × 10⁻³ m (amplitude is the maximum displacement from equilibrium, not the crest-to-trough distance). Speed: c = fλ = (2.5 Hz)(1.5 m) = 3.75 m s⁻¹ = 3.8 m s⁻¹ (2 s.f., matching the data). Check/Trap: if the question quotes a peak-to-peak value of 12 mm, halve it; and never take λ from the time graph.

51. Worked problemSL & HLData booklet: No – memorise

    Two points on a progressive wave of wavelength 1.2 m are 0.30 m apart. Calculate the phase difference between the oscillations at these two points, in radians and in degrees.

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    Principle: phase difference Δφ = 2π × (Δx/λ), where Δx is the separation along the direction of propagation. Substitute: Δx/λ = 0.30 m / 1.2 m = 0.25, i.e. a quarter of a wavelength. Radians: Δφ = 2π × 0.25 = π/2 rad = 1.6 rad (2 s.f.). Degrees: Δφ = 360° × 0.25 = 90°. Check/Trap: a separation of one whole wavelength gives 2π rad (in phase) and half a wavelength gives π rad (antiphase), so a quarter wavelength must give π/2 — quote the unit. A separation of 1.5 m (1.25λ) would give the same phase difference, because phase repeats every 2π.

52. Worked problemSL & HLData booklet: Yes

    The amplitude of the wave from a small isotropic source is doubled while a detector is moved from 1.0 m to 3.0 m from the source. Determine the factor by which the intensity at the detector changes.

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    Principle: two proportionalities from the data booklet — I ∝ A² and I ∝ x⁻². Amplitude effect: doubling A multiplies I by 2² = 4. Distance effect: trebling x multiplies I by (1/3)² = 1/9. Combined: I₂/I₁ = 4 × 1/9 = 4/9 = 0.44 (2 s.f.). Answer: the intensity falls to about 0.44 of its original value, i.e. a decrease of about 56 %. Check/Trap: apply the two factors as a product, not a sum; and remember the inverse square uses the ratio of distances, so it is (1/3)² and not 1/3. If instead the amplitude had trebled, the two effects would cancel exactly.

53. Worked problemSL & HLData booklet: Yes

    A small lamp emits 60 W of light energy uniformly in all directions. Calculate the intensity of the light at a distance of 2.0 m from the lamp.

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    Principle: for a point source the power spreads over a sphere of area 4πx², so I = P/(4πx²) (the booklet form of I ∝ x⁻²). Substitute: I = 60 W / (4π × (2.0 m)²) = 60 / (4π × 4.0) = 60 / 50.27 m². Answer: I = 1.19 W m⁻² ≈ 1.2 W m⁻² (2 s.f.). Check/Trap: square the distance, not just the radius term — using 4π × 2.0 gives 2.4 W m⁻², a classic error. Also note the wording: if the question says a 60 W lamp with 5 % efficiency, the radiated light power is only 3.0 W and I = 0.060 W m⁻².

54. Worked problemSL & HLData booklet: No – memorise

    A student stands 150 m from a large wall, claps once and hears the echo 0.88 s later. Determine the speed of sound in air and estimate the percentage uncertainty if the timing is uncertain by ±0.05 s.

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    Principle: speed = distance/time, where the sound travels to the wall and back, so d = 2 × 150 m = 300 m. Substitute: v = 300 m / 0.88 s = 340.9 m s⁻¹ = 3.4 × 10² m s⁻¹ (2 s.f.). Uncertainty: fractional uncertainty in t = 0.05/0.88 = 5.7 %; if the distance is known to ±1 m that adds 0.7 %, giving about 6 % overall, i.e. v = (3.4 ± 0.2) × 10² m s⁻¹. Check/Trap: forgetting the factor of two halves the answer to 170 m s⁻¹. Improvement: time 20 successive claps synchronised with the echoes and divide, which reduces the reaction-time uncertainty by a factor of 20.

55. Worked problemSL & HLData booklet: Yes

    Five complete waves pass a fixed point on a rope in 4.0 s, and the distance between successive crests is 0.80 m. Determine the frequency, the period and the speed of the waves.

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    Principle: f = number of cycles/time, T = 1/f (data booklet), c = fλ (data booklet). Frequency: f = 5 / 4.0 s = 1.25 Hz. Period: T = 1/1.25 = 0.80 s. Wavelength: λ = crest-to-crest distance = 0.80 m. Speed: c = fλ = 1.25 × 0.80 = 1.0 m s⁻¹ (2 s.f.). Answer: f = 1.3 Hz, T = 0.80 s, c = 1.0 m s⁻¹. Check/Trap: the numerical coincidence that T and λ are both 0.80 is a trap — they have different units and different meanings. Also, "five waves pass in 4.0 s" means five whole cycles, so do not use four.

56. Worked problemSL & HLData booklet: Yes

    Two identical small lamps are viewed from distances of 2.0 m and 5.0 m. Determine the ratio of the intensity received from the nearer lamp to that from the further lamp.

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    Principle: for identical point sources of the same power, I ∝ x⁻² (data booklet), so I₁/I₂ = (x₂/x₁)². Substitute: I₁/I₂ = (5.0 m / 2.0 m)² = (2.5)². Answer: I₁/I₂ = 6.25 ≈ 6.3 (2 s.f.); the nearer lamp appears about 6 times more intense. Since I ∝ A², the amplitude ratio is √6.25 = 2.5, i.e. simply the inverse ratio of the distances. Check/Trap: invert the ratio the right way — the nearer source must be brighter, so the larger distance goes on top. This is exactly the astronomy relation b = L/(4πd²) applied to two stars of equal luminosity.

57. Worked problemSL & HLData booklet: Yes

    A microwave oven emits radiation of frequency 2.45 GHz. Calculate the wavelength of this radiation and state which region of the electromagnetic spectrum it lies in.

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    Principle: all EM waves travel at c = 3.00 × 10⁸ m s⁻¹ in air/vacuum, and c = fλ (data booklet). Substitute: λ = c/f = (3.00 × 10⁸ m s⁻¹)/(2.45 × 10⁹ Hz). Intermediate: 3.00/24.5 = 0.12244…, so λ = 0.122 m (3 s.f.), about 12 cm. Region: microwave — consistent with the quoted frequency. Check/Trap: 1 GHz = 10⁹ Hz; writing 2.45 × 10⁶ gives 122 m, which would be a radio wave and should immediately look wrong. A useful sanity check is that this wavelength explains why microwave-oven door meshes have holes of a few millimetres, far smaller than 12 cm.

58. Worked problemSL & HLData booklet: Yes

    In a ripple tank, 20 wavefronts pass a fixed point in 8.0 s and adjacent wavefronts are 2.5 cm apart. Determine the frequency and speed of the water waves, and the time for a wave to cross a 1.5 m tank.

    Show answer

    Principle: successive wavefronts are one wavelength apart, so λ = 2.5 cm = 0.025 m. Frequency: f = 20/8.0 s = 2.5 Hz; period T = 1/f = 0.40 s. Speed: c = fλ = 2.5 Hz × 0.025 m = 0.0625 m s⁻¹ = 6.3 × 10⁻² m s⁻¹ (2 s.f.). Crossing time: t = d/c = 1.5 m / 0.0625 m s⁻¹ = 24 s. Check/Trap: convert cm to m before using c = fλ, or the speed comes out 100 times too large. Note that if the tank water is made shallower the speed and wavelength both fall while the dipper frequency, set by the motor, stays at 2.5 Hz.

59. Worked problemSL & HLData booklet: No – memorise

    A wave of wavelength 1.8 m travels along a stretched spring. Determine the smallest separation of two points on the spring whose oscillations differ in phase by π/3 rad.

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    Principle: Δφ = 2πΔx/λ, so Δx = λ Δφ/(2π). Substitute: Δx = (1.8 m)(π/3)/(2π) = 1.8/6 m. Answer: Δx = 0.30 m. Equivalently π/3 rad is one sixth of a cycle (60°), and one sixth of 1.8 m is 0.30 m. Check/Trap: the question says smallest — separations of 0.30 m + nλ (2.1 m, 3.9 m …) give the same phase difference, so quote 0.30 m. Convert consistently: if the phase difference is given as 60°, use Δx = λ × 60/360. A quick check: half a wavelength (0.90 m) must correspond to π rad, and 0.30 m is a third of that, matching π/3.

60. Worked problemSL & HLData booklet: No – memorise

    During a storm a student sees a lightning flash and hears the thunder 4.5 s later. Taking the speed of sound in air as 340 m s⁻¹, determine the distance to the lightning and justify neglecting the travel time of the light.

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    Principle: the light and sound travel the same distance d; the delay is the difference in travel times. Sound: t_sound = d/340. Light: t_light = d/(3.00 × 10⁸). Assume t_light ≈ 0, so d ≈ 340 m s⁻¹ × 4.5 s = 1530 m = 1.5 × 10³ m (2 s.f.). Justification: t_light = 1530/(3.00 × 10⁸) = 5.1 × 10⁻⁶ s, which is about 10⁻⁶ of the measured delay and far below the student's reaction time (~0.2 s), so it is negligible. Check/Trap: the reaction-time uncertainty of ±0.2 s gives about ±4 %, i.e. ±70 m — quote the answer to 2 s.f. only. The familiar rule "3 s per kilometre" follows from 1/340.

61. Exam technique/trapSL & HL

    Outline what the command terms state, describe, outline, explain, determine, deduce, sketch, suggest and compare require in C.2 wave-model questions.

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    • State: give a fact with no reasoning — "the frequency is unchanged"
    • Describe: give a detailed account without reasons — the shape of a graph, the motion of a cork
    • Outline: a brief account of the main points
    • Explain: give reasons or causes — the marks are in the because clauses, so every statement needs a physical justification
    • Determine/calculate: a numerical answer with working, unit and appropriate significant figures
    • Deduce: reach a conclusion from given data and state the reasoning chain
    • Sketch: a labelled graph with correct shape, axes and any key intercepts, but no accurate plotting
    • Suggest: propose a plausible answer for an unfamiliar situation
    • Compare: give similarities and differences, using comparative language ("whereas", "both"). Exam tip: an "explain" answer written as a bare statement scores at most one of the available marks.
62. Exam technique/trapSL & HL

    A snapshot (displacement–distance) graph of a transverse wave is given, together with the direction in which the wave is travelling. Explain the correct method for finding the instantaneous direction of motion of a particular particle, and the trap students fall into.

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    The trap: students draw the particle's velocity along the direction of wave travel, or simply say it moves "towards the nearest crest". Why: the snapshot looks like a picture of motion, so the eye follows the wave rather than the particle. Correct approach: the wave shape moves bodily in the stated direction, so after a very short time the particle takes the displacement currently held by the point just behind it — i.e. the point on the side from which the wave has come. If the wave travels to the right, look immediately to the left of the particle: if that point is higher, the particle is moving up. Particles always move perpendicular to the propagation direction, never along it, and particles at a crest or trough are momentarily at rest. Exam tip: mark schemes accept a clear arrow with the reasoning "the wave moves right so P takes the displacement of the point to its left".

63. Exam technique/trapSL & HL

    Explain the trap of confusing displacement–distance and displacement–time graphs, and how to avoid losing marks.

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    The trap: students read a wavelength off a time axis or a period off a distance axis, then compute c = fλ with mismatched quantities. Why: the two sine curves are visually identical and IB deliberately gives them without stating which is which. Correct approach: the first thing to check is the x-axis label and unit — metres/centimetres means it is a snapshot of the whole wave, so the horizontal repeat distance is λ; seconds/milliseconds means it follows one particle, so the horizontal repeat is T. Amplitude can be read from either. Only when you have λ from one graph and T (hence f = 1/T) from the other can you use c = fλ. Exam tip: if a question supplies both graphs, it is almost always testing exactly this — write "from the distance graph λ = …" and "from the time graph T = …" explicitly to secure the method marks.

64. Exam technique/trapSL & HL

    Explain the trap in questions where a wave crosses a boundary between two media, and set out the correct reasoning.

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    The trap: students assume that because the wave slows down, its frequency falls, or that the wavelength stays the same. Why: the intuitive picture is that "slower means fewer waves per second". Correct approach: the boundary is driven by the incoming oscillations, so the same number of wavefronts arrive and leave each second — frequency is set by the source and is invariant. Speed is a property of the medium. Therefore, from c = fλ, λ ∝ c: light entering glass of refractive index 1.5 has its speed and wavelength reduced by 1.5 while f, and hence the colour, is unchanged. Sound entering water speeds up, so λ increases. Exam tip: write the chain "f constant → c changes → λ changes in the same ratio"; a common follow-up asks why a submerged object looks a different size, not a different colour.

65. Exam technique/trapSL & HL

    Design an experiment to measure the speed of sound in air, identifying apparatus, variables, sources of uncertainty and improvements.

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    Method (two-microphone): mount two microphones a measured distance d apart on a metre rule, connect to a fast timer or a dual-trace oscilloscope/data logger, and produce a sharp sound (hammer on metal plate) beyond the first microphone; the timer measures Δt between the two signals; v = d/Δt. Independent variable d, dependent variable Δt, controlled: air temperature, microphone alignment and gain. Plot d against Δt: the gradient is v, and a straight line through the origin confirms constant speed. Uncertainties: d to ±1 mm (small fractional uncertainty if d ≈ 1 m); timing resolution dominates, so use the largest workable d. Limitations: draughts, echoes from walls, temperature drift. Improvements: repeat and average, work outdoors or in a large room to avoid reflections, record the temperature since v ∝ √T. Exam tip: an echo/stopwatch method must include reaction-time uncertainty and multiple claps.

66. Exam technique/trapSL & HL

    Describe how to measure the speed of water waves in a ripple tank, and evaluate the method.

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    Method: set the motorised dipper to a fixed frequency f read from the motor setting or by timing 20 oscillations with a stopwatch (f = 20/t). Photograph or strobe the pattern with a metre rule lying in the tank in the same plane as the water surface, then measure the distance across 10 wavefronts and divide by 10 to get λ. Calculate v = fλ. Independent variable: water depth; controlled: frequency, dipper amplitude, tank levelling. Uncertainties: measuring across many wavelengths reduces the fractional uncertainty in λ; parallax between the rule and the projected image is the main systematic error, reduced by placing the rule at the water surface and photographing from directly above. Limitations: the pattern is not perfectly sharp and reflections from the tank walls interfere. Improvement: use video at a known frame rate and step through frames. Exam tip: never measure a single wavelength.

67. Exam technique/trapSL & HL

    Explain how to handle absolute, fractional and percentage uncertainties when calculating a wave speed from c = fλ, and state the significant-figure rule.

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    • Absolute uncertainty has the same unit as the quantity (λ = 0.660 ± 0.005 m); fractional uncertainty is Δλ/λ; percentage uncertainty is 100 × Δλ/λ
    • For a product or quotient, add the fractional (or percentage) uncertainties: Δc/c = Δf/f + Δλ/λ
    • For a sum or difference, add the absolute uncertainties
    • For a power, multiply the fractional uncertainty by the exponent — so for I ∝ A², ΔI/I = 2 ΔA/A
    • Quote the uncertainty to one significant figure, then round the value to the same decimal place: c = (341 ± 6) m s⁻¹, not 340.909 ± 5.83
    • The final answer's significant figures should match the least precise datum, usually 2 or 3 in IB. Exam tip: marks are lost for an answer given to the calculator's full display, and for omitting the unit on the uncertainty.
68. Exam technique/trapSL & HL

    Explain how to use error bars and maximum/minimum gradients on a wave graph, and distinguish random from systematic error and precision from accuracy.

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    • Plot the points with vertical (and, if significant, horizontal) error bars showing the absolute uncertainty
    • Draw the best-fit line, then the steepest and shallowest lines that still pass through every error bar
    • The gradient uncertainty is Δm = (m_max − m_min)/2, and the result is quoted as m ± Δm
    • Random error scatters points either side of the line and is reduced by repeating and averaging — for example reaction time in stopwatch timing of wave pulses
    • Systematic error shifts every point the same way, producing a non-zero intercept where the theory predicts one through the origin — for example a zero error on a metre rule or a delayed trigger
    • Precise means repeatable (small scatter); accurate means close to the true value
    • A precise but inaccurate data set gives tight points along a displaced line. Exam tip: a non-zero intercept on a d–Δt graph is the classic "identify the systematic error" mark.
69. Exam technique/trapSL & HL

    Outline what a "sketch" answer must show when asked to sketch wave graphs in C.2, and the marks usually available.

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    • Label both axes with the quantity and unit — displacement/m against distance/m or time/s
    • Show the correct shape: a smooth sinusoid of constant amplitude and constant wavelength/period for a progressive wave
    • Mark the amplitude and one full wavelength or period on the graph with a labelled double-headed arrow if the question names them
    • For two waves with a stated phase difference, keep the same amplitude and period and shift the second curve horizontally by the correct fraction of a cycle
    • For pressure and displacement graphs of a sound wave, show the quarter-cycle (90°) shift
    • For intensity against distance from a point source, show a decreasing curve that is concave up and never touches the x-axis
    • Sketches need no plotted points but must be qualitatively right. Exam tip: unlabelled axes or an amplitude that decays when nothing said it should are the usual reasons for losing the mark.

Practise this topic with exam-style questions: C.2 Wave model questions (SL) · C.2 Wave model questions (HL) · all flashcards

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