Generated ERQ

✓ passed C.2 Wave model × D.2 Electric and magnetic fields 10 marks SL 3 passes 128.73s $0.7443

``` ## ERQ · 10 marks · Topics: C.2 Wave model + D.2 Electric and magnetic fields · Archetype: data_response **Integration:** primary=C.2 Wave model, secondary=D.2 Electric and magnetic fields (strength: supporting) **Stem.** A moving-coil loudspeaker produces sound by passing an alternating current through a cylindrical coil suspended in the radial magnetic field of a permanent magnet. The current-carrying coil experiences a force *F = BIL* that drives a paper cone, which oscillates and radiates longitudinal sound waves into the air. A technician measures the cone's motion using a laser displacement sensor while driving the speaker with a pure tone. The recorded data are summarised below. | Quantity | Symbol | Value | |---|---|---| | Driving frequency | *f* | 440 Hz | | Peak displacement of cone | *x₀* | 1.5 mm | | Mass of moving coil + cone | *m* | 8.0 g | | Magnetic flux density (radial) | *B* | 0.65 T | | Length of wire in field | *L* | 4.8 m | | Peak coil current | *I₀* | 0.45 A | | Speed of sound in air | *v* | 340 m s⁻¹ | ### Part (a) State [2 marks] · AO1 · Topic: C.2 State the wave equation relating speed, frequency and wavelength, and define what is meant by the *wavelength* of a longitudinal sound wave. ### Part (b) Calculate [2 marks] · AO2 · Topic: C.2 Calculate the wavelength of the 440 Hz sound wave emitted into the air. ### Part (c) Calculate [2 marks] · AO2 · Topic: C.2 Assuming the cone oscillates with simple harmonic motion at 440 Hz with peak displacement 1.5 mm, calculate the peak acceleration of the cone. ### Part (d) Evaluate [4 marks] · AO3 · Topic: C.2 + D.2 · ASSUMPTIONS DISCRIMINATOR Using the data in the table, evaluate whether the magnetic force *F = BIL* on the coil is sufficient to sustain the SHM described in (c), and suggest **one** further reason why the SHM model may break down at very large cone amplitudes. --- ## Mark Scheme ### Part (a) [2 marks] - M1: *v = fλ* stated (symbols defined or in standard form) [no ECF] - M2: wavelength = distance between two consecutive points in the wave that are in phase / distance between two consecutive compressions (or rarefactions) [no ECF] ### Part (b) [2 marks] — Calculate - M1: correct rearrangement and substitution λ = v/f = 340/440 [no ECF] - M2: λ = 0.77 m (accept 0.773 m) [no ECF] ### Part (c) [2 marks] — Calculate - M1: use of *a*_max = ω²x₀ with ω = 2π × 440 (= 2765 rad s⁻¹), substitution into (2π × 440)² × 1.5 × 10⁻³ [no ECF from (b)] - M2: *a*_max ≈ 1.15 × 10⁴ m s⁻² (accept 1.1–1.2 × 10⁴ m s⁻²) [no ECF] *Note: a common student error is to omit the 10⁻³ conversion of x₀; award M1 only.* ### Part (d) [4 marks] — Evaluate (judgement + supporting + limiting per §4.4.1) - M1: required peak force *F*_req = *m a*_max = 0.0080 × 1.15 × 10⁴ ≈ 92 N [ECF from (c)] - M2: magnetic force available *F* = *BIL* = 0.65 × 0.45 × 4.8 ≈ 1.4 N [no ECF] - M3: judgement — the available magnetic force is roughly **two orders of magnitude smaller** than the force required, therefore the coil **cannot** sustain pure SHM at 1.5 mm amplitude with this current / the stated motion is inconsistent with the electromagnetic drive [ECF from M1, M2] - M4: ONE valid physical reason the SHM model breaks down at large amplitudes, e.g.: - the restoring force of the cone suspension becomes non-linear (Hooke's law fails) at large *x*, OR - the coil partially leaves the region of uniform radial *B*, so *F = BIL* no longer gives a force proportional to *I* (and hence not proportional to displacement), OR - significant air-loading / acoustic radiation damping at large amplitude removes energy from the oscillator each cycle ### Marker notes - (a) M2: do not credit "the length of one wave" without reference to phase or compressions/rarefactions. - (b) accept λ to 2 or 3 sf. - (c) accept *a*_max via *a* = (2πf)²x₀ in a single step; both marks awarded if correct value reached. - (d) M3: ECF — if a candidate's M1 value is wrong, award M3 provided their stated *F*_req is correctly compared with their *F* and a consistent judgement is made. - (d) M4: accept any one well-justified mechanism from the bullet list; do NOT award a bare statement such as "SHM fails" without a physical mechanism. - (d) full marks possible even if candidate concludes correctly that the listed current must in reality be larger (e.g. peaks > 60 A) — the key AO3 step is recognising the inconsistency. ```

Critic verdicts

Iteration 0 — failed

ao_ladder pass

The ERQ obeys the cognitive ladder correctly. Part (a) is AO1 (Define/Outline) with command term Outline; parts (b) and (c) are AO2 (Calculate/Show that) with appropriate procedural demands; part (d) is AO3 (Suggest) requiring reasoned proposal with physics justification. The progression from recall→calculation→application is proper, and discrimination between routes at the top tier is pedagogically sound.
command_structure warning

critic parse error: Unterminated string starting at: line 6 column 20 (char 885); raw: ```json { "passed": false, "severity": "fail", "reasoning": "Part (d) mark scheme violates §4.4.1 AO3 'Suggest' co
cross_theme fail

Part (d) fails the blending dimension. Although D.2 (magnetic field geometry) is mentioned as an alternative route, the primary physics content of the question is entirely C.2 (wave motion, SHM, wavelength, frequency). D.2 appears only as one optional justification path in the final part and is not genuinely integrated into the problem—students can answer all of (a)–(c) and most of (d) without engaging with electric and magnetic fields at all. The magnetic field is used only as a label for the driving mechanism in the stem; it does not actually feature in solving the wave-based calculations or even in the primary (Route B) suggested answer.

FIX: Restructure the question so that D.2 (magnetic fields) is essential to the core solution, not optional. For example: ask students to calculate the force F = BIL required to produce the observed acceleration in part (c), then discuss how the finite width of the magnetic field gap limits the force available at large displacements (forcing them to use both C.2 and D.2 quantitatively). Alternatively, add a part asking how the magnetic force amplitude varies with coil position and how this deviation from linearity explains the breakdown of SHM—making the D.2 content integral to the reasoning chain, not just an appendix.
discriminator pass

Part (d) explicitly asks students to 'suggest one reason why... the assumption of pure simple harmonic motion of the cone breaks down' and requires reference to either magnetic field geometry or wave behaviour. This is a clear model-critique task that goes beyond calculation—it demands students to identify a physical limitation and justify why linearity fails.
rule_of_one pass

Each part's mark count matches the number of distinct award criteria listed. Part (a): 2 marks, 2 bullets (definition + relationship). Part (b): 3 marks, 3 bullets (rearrangement/substitution, numerical answer, comparison comment). Part (c): 3 marks, 3 bullets (formula identification, substitution of ω, final answer with working). Part (d): 2 marks, 2 bullets per route (proposal + justification). All align correctly.
topic fail

Part (d) nominally names both topics but fails the substance test. The question asks students to suggest **one** reason (not both), and the mark scheme explicitly accepts either Route A (D.2 magnetic field) OR Route B (C.2 wave behaviour)—not both. A student can earn full marks by choosing only one topic, meaning D.2 Electric and magnetic fields is not actually required for the question. This violates the dimension's requirement that both topics must be genuinely necessary.

FIX: Restructure part (d) to require students to explain **both** the magnetic field geometry breakdown (D.2) and the nonlinear air loading effect (C.2) as complementary mechanisms, or split into two sub-questions: (d-i) magnetic field effect; (d-ii) wave behaviour effect. Alternatively, reframe the integration in the metadata as 'secondary: optional' if only one topic is meant to be tested.

Iteration 1 — failed

ao_ladder fail

The cognitive ladder is broken at part (c). Part (c) is marked as AO2 'Show that' but requires AO3-level reasoning: students must compute F_req, compare it to F = BIL, and critically evaluate why the magnetic force is insufficient (a conceptual judgement). This is NOT AO2 calculation—it is AO3 evaluation. Additionally, part (d) 'Suggest' is correctly AO3, but placing AO3 reasoning in the middle tier violates the ladder structure.

FIX: Restructure as follows: (a) State [2 marks] AO1; (b) Calculate [2 marks] AO2 for frequency and wavelength only; (c) Calculate [2 marks] AO2 to find a_max and F = BIL numerically without comparison; (d) Explain/Evaluate [4 marks] AO3 combining the force insufficiency (D.2 context) with the two physical reasons for SHM breakdown. Alternatively, move the force-comparison logic to part (d) and rewrite (c) to ask only 'Calculate the peak acceleration and peak magnetic force' without the 'show it is large enough' judgment.
command_structure fail

Part (c) mark scheme violates §4.2: M3 awards a mark for stating the formula F = BIL alone without establishing it as a marking point. Additionally, the 'Show that' structure is internally inconsistent—M3 requires computation of both F and F_req with a comparison/comment, but this conflates a formula statement with reasoning and makes the target 'show that' unclear. Part (d) satisfies §4.4.1 (Suggest = proposal + reasoning in both M1 and M2), but part (c) fails the core dimension.

FIX: Restructure part (c) M3 as follows: (M3a) 'F = BIL = 0.65 × 0.45 × 4.8 = 1.40 N' [ECF from (b)]; (M3b) 'F_req = m·a_max = 0.008 × 1.15 × 10³ = 9.2 N; candidate must state that BIL force (1.40 N) is insufficient by factor ~6 compared to required force (9.2 N), hence the quoted I₀ is insufficient for the stated motion.' Alternatively, clarify in M3 that the 'show that' target is demonstrating the *insufficiency* of the BIL force, not merely its magnitude, and award the mark only when the comparison and conclusion are explicit. Do not award a mark for F = BIL formula statement alone.
cross_theme pass

The question genuinely blends C.2 (Wave model) and D.2 (Electric and magnetic fields) across multiple parts. Part (c) requires both the wave-based SHM equation (a_max = ω²x₀, derived from frequency in part b) AND the magnetic force law (F = BIL from D.2) to solve the problem. Part (d) then explicitly demands one D.2 mechanism (magnetic-field geometry causing non-linearity in F) and one C.2 mechanism (wave behaviour/air compression causing non-linearity in restoring force). Neither topic is filler; both are essential to the physics.
discriminator pass

Part (d) explicitly asks students to suggest reasons why the motion departs from simple harmonic motion under high-volume conditions, requiring critique of two model assumptions: the magnetic-field geometry (D.2) and wave behaviour of air (C.2). This is authentic model critique asking students to identify and explain limitations of the idealized SHM treatment.
rule_of_one fail

Part (c) mark count (3 marks) does not match award criteria count (4 bullets: M1 contains two distinct operations, M2, M3 contains verification step). M1 requires both ω calculation AND formula application (2 operations), and M3 requires computing F, F_req, AND comparison (3 operations). The structure is fragmented across bullets and exceeds 3 clear award criteria.

FIX: Restructure part (c) to align 3 marks with exactly 3 distinct operations: (M1) Calculate ω = 2πf from frequency in (b) [1 mark]; (M2) Calculate a_max = ω²x₀ = 1.15 × 10³ m s⁻² [1 mark]; (M3) Calculate required force F_req = ma_max ≈ 9.2 N and compare with F = BIL = 1.40 N, noting insufficiency [1 mark]. Alternatively, if the intent is to award the BIL calculation and the a_max calculation separately, add a 4th mark and retitle as [4 marks] — Calculate.
topic pass

The ERQ substantively tests both C.2 (Wave model) and D.2 (Electric and magnetic fields). Parts (a)–(b) establish wavelength and wave speed concepts (C.2). Part (c) integrates both: it requires SHM analysis of the cone (C.2) and applies the magnetic force law F = BIL (D.2) to verify whether the force is sufficient. Part (d) explicitly demands one failure mode from D.2 (non-uniform B field geometry) and one from C.2 (non-linear air compression), ensuring both topics are genuinely invoked to explain departures from ideality. Neither topic is merely nominal.

Iteration 2 — failed

ao_ladder pass

The ERQ obeys the cognitive ladder correctly. Part (a) is AO1 (State), part (b) is AO2 (Calculate), part (c) is AO2 (Calculate), and part (d) is AO3 (Evaluate + Suggest). The progression from knowledge recall → procedural calculation → analytical evaluation is strict and appropriate for SL 10-mark data-response.
command_structure fail

Part (d) mark scheme violates §4.4.1 AO3 structure for Evaluate. M3 provides position + supporting consideration but lacks an explicit limiting consideration. M4 is a suggestion (proposal + justification) but Evaluate requires position + support + limit. The scheme conflates two distinct command terms without meeting Evaluate's full three-component structure.

FIX: Restructure Part (d) to clearly separate the AO3 commands: (i) retain M1–M3 as the Evaluate component (position: force insufficient; supporting: quantitative comparison showing ~100× gap), then add an explicit limiting consideration such as 'however, the model assumes ideal conditions and does not account for...' or 'this analysis neglects potential measurement uncertainty in B, I, or L'; (ii) designate M4 as a distinct Suggest part ('Suggest one reason...') with its own 1 mark, making clear that Suggest requires proposal + brief justification (which it does provide). Alternatively, if M4 must remain in Part (d), reframe M3 to include both a supporting AND a limiting perspective (e.g., 'the force is insufficient under the assumption of constant B and sinusoidal current, but in practice the current waveform or field geometry may differ') before M4 addresses a separate breakdown mechanism.
cross_theme fail

Part (d) uses D.2 (magnetic force F = BIL) only as a calculation tool and numerical comparison, but does NOT genuinely integrate both physics concepts in solving the core problem. The wave model (C.2) is applied in parts (a)–(c) independently; part (d) then bolts on a magnetic force check as an 'assumptions discriminator' without requiring students to explain how the electromagnetic drive and wave propagation interact. M4 asks for a physical reason SHM breaks down but explicitly divorces this from the magnetic field physics—the three suggested answers mention suspension nonlinearity, coil leaving the field, or air damping, none of which genuinely blend C.2 and D.2 in a unified analysis. The question reads as: 'solve the wave problem, then separately check if the magnetic force is adequate'—not 'use both concepts together to solve one problem.'

FIX: Reframe part (d) to require students to explain how the interaction between the electromagnetic driving force and acoustic impedance (or cone-air coupling) affects the actual motion. For example: 'The impedance of the air changes the effective mass and damping seen by the coil. Using the given B, I₀, and L, estimate the acoustic power radiated by the cone, and determine whether the available electromagnetic power can sustain radiation at the stated amplitude. Comment on how the magnetic force, frequency, and wave properties together constrain the maximum amplitude.' This forces genuine integration: D.2 (force generation) + C.2 (wave energy/impedance) must both be used in a single reasoning chain.
discriminator pass

Part (d) explicitly requires students to evaluate whether the magnetic force model is sufficient and to suggest one reason why the SHM model breaks down at large amplitudes. This is a genuine model-critique question asking students to identify limitations (non-linear restoring force, non-uniform field effects, air damping) rather than just perform calculations.
rule_of_one warning

critic parse error: Expecting ',' delimiter: line 5 column 529 (char 572); raw: ```json { "passed": false, "severity": "fail", "reasoning": "Part (d) is marked as [4 marks] but contains 4 distin
topic pass

The ERQ genuinely integrates both topics. Part (d) is the critical evaluative question that requires candidates to use wave-model concepts (SHM, acceleration from part c) alongside electromagnetic field concepts (magnetic force F = BIL, field uniformity). The contradiction revealed—that the available magnetic force is two orders of magnitude smaller than required—is inherently a C.2 + D.2 synthesis problem, not a superficial mention.

Planner output (stage 1)

Archetype: real-world device
Scenario: A moving-coil loudspeaker converts electrical signals into sound waves by passing current through a coil suspended in a magnetic field. The coil oscillates perpendicular to a radial magnetic field, driving a cone that produces sound. Students analyse the wave properties of the emitted sound and the electromagnetic principles governing the coil's motion.
Cross-pollination part: d
Discriminator part: d

Part	Marks	AO	Command
a	2	AO1\|AO2	Define the term wavelength and state the relationship between wave speed, frequency and wavelength.
b	3	AO2\|AO3	A loudspeaker emits sound at 440 Hz (note A). Given the speed of sound in air is 340 m s⁻¹, calculate the wavelength of the emitted sound wave.
c	3	AO2\|AO3	The coil in the loudspeaker has a mass of 8.0 g and moves with maximum displacement amplitude of 1.5 mm at 440 Hz. Show that the maximum acceleration of the coil is approximately 1.2 × 10³ m s⁻².
d	2	AO3	The force on the coil is provided by F = BIL, where B is the magnetic flux density, I is the current, and L is the length of the coil in the field. Suggest why the assumption of simple harmonic motion for the loudspeaker cone becomes less valid at very high amplitudes, considering both the wave properties and the electromagnetic forces involved.

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