Generated ERQ

✓ passed C.2 Wave model × A.1 Kinematics 12 marks SL 3 passes 114.55s $0.7668

## ERQ · 12 marks · Topics: C.2 Wave model + A.1 Kinematics · Archetype: experimental_analysis **Integration:** primary=C.2 Wave model, secondary=A.1 Kinematics (strength: supporting) **Stem.** A student investigates water waves in a rectangular ripple tank of length 0.80 m. A vertical dipper attached to a motor generates plane waves at one end of the tank; a stroboscope is used to "freeze" the wave pattern so that wavelengths can be measured on a scale beneath the tank. The student sets the motor frequency to f = 5.0 ± 0.1 Hz and, with the stroboscope adjusted, measures the distance across 6 successive crests as 0.150 ± 0.002 m. In a second procedure, the student instead measures the time taken for a single disturbance (made by tapping the water once) to travel the full 0.80 ± 0.01 m length of the tank, obtaining t = 5.4 ± 0.4 s. Finally, the student mounts the dipper on a small trolley moving with constant velocity 0.10 m s⁻¹ along the tank, in the same direction as the wave travel, and asks how the observed wavelength ahead of the trolley would change. ### Part (a) Define [2 marks] · AO1 · Topic: C.2 Wave model Define (i) wavelength and (ii) frequency for a travelling wave. ### Part (b)(i) Calculate [3 marks] · AO2 · Topic: C.2 Wave model Using the measurements from the stroboscope procedure, calculate the speed of the water waves in the tank. ### Part (b)(ii) Determine [2 marks] · AO2 · Topic: C.2 Wave model + A.1 Kinematics Using the single-disturbance timing procedure, determine a second value for the wave speed. ### Part (c) Comment on [3 marks] · AO3 · Topic: C.2 Wave model By propagating the relevant uncertainties, comment on whether the two values of wave speed obtained in (b)(i) and (b)(ii) are consistent. ### Part (d) Discuss [2 marks] · AO3 · ASSUMPTIONS DISCRIMINATOR · Topic: C.2 Wave model + A.1 Kinematics With the dipper now moving on the trolley at 0.10 m s⁻¹, the student claims the relation v = fλ predicts that the wavelength ahead of the trolley becomes (v − v_source)/f. Discuss one assumption underlying this prediction whose breakdown in a real ripple tank could limit its validity. --- ## Mark Scheme ### Part (a) [2 marks] - M1: Wavelength = shortest distance between two points on the wave oscillating in phase / distance between successive crests [no ECF] - M2: Frequency = number of complete oscillations (of a point in the medium / of the source) per unit time [no ECF] ### Part (b)(i) [3 marks] — Calculate - M1: Recognises that 6 crests span 5 wavelengths, so λ = 0.150 / 5 = 0.030 m [no ECF] - M2: Correct substitution into v = fλ = 5.0 × 0.030 [no ECF] - M3: v = 0.15 m s⁻¹ (accept 0.150 m s⁻¹) [ECF from M1] ### Part (b)(ii) [2 marks] — Determine - M1: Uses v = d/t with d = 0.80 m, t = 5.4 s [no ECF] - M2: v = 0.148 ≈ 0.15 m s⁻¹ [ECF from M1] ### Part (c) [3 marks] — Comment on (evidence-tied interpretation) - M1: Fractional uncertainty in v from (b)(i): Δv/v = Δλ/λ + Δf/f = 0.002/0.150 + 0.1/5.0 ≈ 0.013 + 0.020 = 0.033, giving v₁ = 0.15 ± 0.005 m s⁻¹ [ECF from (b)(i)] - M2: Fractional uncertainty in v from (b)(ii): Δv/v = Δd/d + Δt/t = 0.01/0.80 + 0.4/5.4 ≈ 0.013 + 0.074 = 0.087, giving v₂ = 0.15 ± 0.013 m s⁻¹ [ECF from (b)(ii)] - M3: Ranges (0.145–0.155) and (0.135–0.161) m s⁻¹ overlap, therefore the two measurements ARE consistent within experimental uncertainty [ECF from M1, M2] ### Part (d) [2 marks] — Discuss (assumption critique per §4.4.1) - M1: Identifies an assumption — e.g. the wave speed v in water is independent of the source motion / the medium (water) is stationary in the lab frame / the trolley moves at strictly constant velocity / dispersion (frequency-dependence of v) is negligible / reflections from the far end do not interfere with the forward-travelling wave - M2: Explains how its breakdown limits validity — e.g. shallow water waves are dispersive so a change in apparent wavelength would also change v, meaning (v − v_source)/f no longer gives the true observed λ; OR if the trolley accelerates over its short run, v_source in the formula is not well-defined kinematically; OR reflections superpose with outgoing waves so the "wavelength ahead" cannot be cleanly identified ### Marker notes - Alternative method accepted for (b)(i): student may use λ from any consistent count of crest-to-crest intervals, provided 5 intervals are recognised between 6 crests. - For (c), accept absolute-uncertainty addition method giving similar overlap conclusion; conclusion mark (M3) requires explicit reference to overlap of ranges. - For (d), accept any one well-explained assumption from the list; do NOT award M2 without a physical mechanism linking the assumption to a quantitative or qualitative limitation. Mere restatement of the assumption ≠ M2. - Numerical illustration for (d) (not required for marks): v_source·T = 0.10/5.0 = 0.020 m, predicted λ′ = 0.030 − 0.020 = 0.010 m.

Critic verdicts

Iteration 0 — failed

ao_ladder pass

The ERQ obeys the cognitive ladder correctly. Part (a) is AO1 (Define), parts (b)(i)–(b)(ii) are AO2 (Calculate/Determine), and parts (c)–(d) are AO3 (Explain/Suggest). Command terms match cognitive demand at each tier, and the progression from factual recall through procedural calculation to conceptual reasoning and evaluation is strict and appropriate for SL.
command_structure fail

Part (c) mark scheme violates §4.4.1 for Explain command term. M1 states overlap 'therefore' results are consistent, but M2 and M3 do NOT form explicit causal chains—they merely identify error sources without explaining WHY those errors lead to the observed discrepancy or non-discrepancy. The causal link between error magnitude and consistency conclusion is missing.

FIX: Restructure Part (c) M2 and M3 to include explicit causal reasoning. Example: M2 should read: 'The ruler uncertainty (±0.5 cm in 12.0 cm ≈ 4%) propagates to wavelength, **therefore** the calculated wave speed carries ≈ 4% uncertainty ≈ ±0.01 m s⁻¹, **which means** the v = 0.24 m s⁻¹ from (b)(i) has range 0.23–0.25 m s⁻¹.' M3 should read: 'The timing method's dominant error is human reaction time (≈ 0.2 s), **which produces** uncertainty Δv/v ≈ 0.2/3.3 ≈ 6%, **therefore** v = (0.24 ± 0.015) m s⁻¹ ranges 0.225–0.255 m s⁻¹, **so both ranges overlap and results are consistent.**' This ensures each marking point contains at least one 'X therefore Y' causal structure as required by §4.4.1.
cross_theme pass

Both C.2 (Wave model) and A.1 (Kinematics) are genuinely integrated throughout the question. Part (b)(ii) applies kinematics principles (motion equations: v = d/t) to measure wave speed experimentally. Part (d) explicitly requires kinematic reasoning (source velocity, relative motion) to explain the Doppler compression of wavefronts and why measuring compressed wavelengths gives inaccurate wave speed. Neither topic is mere name-checking; both are essential to solving their respective parts.
discriminator pass

Part (d) clearly asks students to critique the model/measurement method by explaining why measuring wavelength in front of a moving dipper would give inaccurate wave speed. The final part explicitly requires conceptual reasoning about the limitation of applying v=fλ when the source is moving, demonstrating model critique rather than mere calculation.
rule_of_one fail

Part (b)(ii) is marked as 2 marks but has 3 distinct award criteria (mean time calculation, velocity calculation, uncertainty calculation with half-range). This exceeds the 2-mark allocation by 1 and violates the dimension's contract that mark count must match award-bullet count within a tolerance of ±1 (here it's +1 in absolute terms, but the uncertainty step is substantial enough to constitute a structural mismatch).

FIX: Either: (1) Split (b)(ii) into two sub-parts: (b)(ii) Calculate mean wave speed [1 mark] and (b)(iii) Determine uncertainty [1 mark]; or (2) Combine the mean time + velocity + uncertainty into a single streamlined 2-mark criterion: 'Calculate mean wave speed (0.24 m s⁻¹) and absolute uncertainty (≈0.02 m s⁻¹) using half-range of timing data', removing the intermediate step as implicit. Option (1) is cleaner and aligns with IB practice.
topic pass

The ERQ authentically integrates both topics. C.2 Wave model is primary (wavelength definition, wave equation v = fλ, wave speed measurement, Doppler-like compression). A.1 Kinematics is genuinely secondary but essential: part (b)(ii) requires mean and uncertainty calculation from motion data; part (d) explicitly demands kinematic reasoning (source velocity affects observed wavelength) to explain why moving-source measurements fail. Neither topic is nominal—both concepts are actively tested.

Iteration 1 — failed

ao_ladder pass

The ERQ exemplifies a well-structured cognitive ladder. Part (a) is AO1 (Define), parts (b)(i)–(b)(iii) are AO2/AO3 with Calculate/Determine, part (c) is AO3 (Explain with causal reasoning), and part (d) is AO3 (Suggest with justification). The progression from recall through calculation to synthesis and evaluation is rigorous and unbroken.
command_structure fail

Part (d) mark scheme violates §4.4.1 'Suggest' structure. M1 states only a proposal (wavelength is shorter) without explicit physics-based justification; M2 provides the justification but is labelled as a separate mark. The structure should be a single integrated marking point: proposal + warrant. Additionally, M1 awards a mark for providing an alternative numerical value λ' = 0.010 m, but this appears to be a formula substitution without independent derivation, risking §4.2 violation (formula alone). The causal chain in M2 ('In time T... therefore... the wavelength is reduced') is present but split across two marks rather than unified.

FIX: Restructure Part (d) as: M1 [1 mark] — 'The wavelength ahead of the trolley is shorter than 0.030 m. The source moves forward by v_source × T = 0.10 × (1/5.0) = 0.020 m during one oscillation period, therefore the successive crests are compressed by this displacement, giving λ' = (v − v_source)/f = (0.15 − 0.10)/5.0 = 0.010 m [ECF from (b)(i)].' [This unifies proposal + kinematic mechanism + result.] M2 [1 mark] — 'This demonstrates that the apparent wavelength observed by a stationary observer ahead of a moving source is reduced according to λ' = (v − v_source)/f, a consequence of the source catching up with its own wavefronts.' Alternatively, award M1 for the kinematic reasoning alone (proposal + mechanism), and only offer the numerical calculation as a worked example in marker notes, not as a standalone marking point.
cross_theme pass

Both C (Wave model) and A (Kinematics) are genuinely integrated throughout the question. C.2 is primary (wave speed, wavelength, frequency relationships), but A.1 kinematics is meaningfully deployed in parts (b)(ii)–(b)(iii) (mean velocity, uncertainty propagation from timing data) and especially in part (d) where the source displacement during one period (Δx = v_source · T, a kinematic quantity) is used to explain wavelength reduction. The second topic is not mere filler—it is essential to calculating speeds and explaining the Doppler-like shift.
discriminator fail

Part (d) asks the student to 'Suggest how the wavelength...would differ' and 'justify your reasoning using kinematics,' but this is a predictive calculation/explanation task, not a critique of the model used. There is no request to critique assumptions, discuss limitations of the wave model, or explain why a discrepancy exists between theory and observation. The final part should ask something like 'Discuss the assumption that the ripple tank is infinitely long' or 'Explain a limitation in treating the trolley motion classically' to satisfy the model-critique dimension.

FIX: Replace part (d) with a question that explicitly asks the student to critique the wave model or the assumptions underlying the experiment. For example: '(d) Discuss one assumption made in the analysis that might affect the validity of the conclusion about whether the two wave-speed measurements are consistent' or '(d) Explain why the simple model v = fλ may not accurately predict the observed wavelength when the source moves, and suggest one physical factor not yet considered.'
rule_of_one fail

Part (c) is marked as 3 marks but lists 4 distinct award criteria (M1, M2, M3, and an implicit causal chain connecting them). More critically, Part (d) is marked as 2 marks but M2 contains both a proposal (wavelength calculation) and detailed reasoning (source displacement mechanism) that should be separated into distinct, countable operations. The mark-to-criterion alignment is broken in both parts.

FIX: Part (c): Consolidate to 3 clear criteria: (M1) propagate ruler uncertainty to wavelength/speed from (b)(i); (M2) state timing uncertainty range from (b)(iii); (M3) compare ranges and conclude consistency or otherwise with justification. Part (d): Separate into 2 explicit criteria: (M1) State that wavelength decreases and ideally give a numerical value or formula; (M2) Explain the mechanism using source displacement: 'source moves v_source·T = v_source/f in one period T, reducing the spacing between successive crests.' This ensures each mark maps to exactly one operation.
topic pass

The ERQ genuinely integrates both topics. C.2 Wave model is the primary focus (wavelength, frequency, v=fλ, wave properties) spanning parts (a)–(d). A.1 Kinematics supports this through displacement-time analysis: (b)(ii) uses distance/time to find speed; (b)(iii) applies uncertainty propagation (Δv/v ≈ Δt/t); and (d) explicitly requires kinematic reasoning about source displacement during one period (v_source·T reduces the wavelength). The Doppler scenario in (d) is framed as a kinematics problem ('justify using kinematics'), not purely as wave superposition, ensuring A.1 is substantively invoked, not nominal.

Iteration 2 — failed

ao_ladder pass

The ERQ correctly obeys the cognitive ladder. Part (a) is AO1 with Define (lowest tier). Parts (b)(i) and (b)(ii) are AO2 with Calculate/Determine (middle tier). Parts (c) and (d) are AO3 with Comment on/Discuss (highest tier), appropriately positioned at the end. The progression is strict and complete across all four tiers.
command_structure fail

Part (d) mark scheme fails the AO3 'Discuss' dimension requirement. Per §4.4.1, 'Discuss' must exhibit 'at least two perspectives or trade-offs,' but the scheme presents only one assumption with its breakdown. The structure shows M1 (identify assumption) and M2 (explain limitation), which is a single perspective critique, not a comparative discussion of multiple viewpoints or competing considerations. The schema conflates 'critique an assumption' with 'discuss,' which are different cognitive tasks.

FIX: Restructure Part (d) to require genuine discussion of two contrasting perspectives: e.g., (M1) 'Assumption A (e.g., stationary medium) and its consequence on the formula,' (M2) 'Assumption B (e.g., non-dispersive water) and its consequence,' with each mark requiring explicit statement of how each assumption's validity affects the prediction differently. Alternatively, reframe Part (d) as 'Evaluate' (position + supporting + limiting consideration) or 'Explain' (causal chain) if only one assumption critique is intended, and relabel accordingly. If the intent is genuinely to discuss two assumptions, add M3 requiring explicit comparison of their relative impact on validity.
cross_theme pass

The ERQ successfully blends both C.2 (Wave model) and A.1 (Kinematics). Part (b)(ii) genuinely requires kinematics (v = d/t, constant velocity motion) to determine wave speed from a timing measurement, not merely as name-checking. Part (d) integrates both themes by requiring students to critique kinematic assumptions (trolley motion, constant velocity) that underpin the Doppler-like prediction v_obs = (v − v_source)/f, where the source velocity is a kinematic quantity. Both physics concepts are essential to the solution.
discriminator pass

Part (d) explicitly asks the student to 'Discuss one assumption underlying this prediction whose breakdown in a real ripple tank could limit its validity.' This is a model-critique task that requires identification of an assumption and explanation of how its violation undermines the formula's applicability—a clear fit to the dimension's requirements.
rule_of_one fail

Part (b)(ii) is marked as 'Determine [2 marks]' but the mark scheme lists only 2 award criteria (M1: uses v=d/t; M2: calculates answer). A 2-mark Determine part typically requires a minimum of 2 distinct operations, which this part satisfies nominally. However, the critical issue is Part (d): it is marked as 'Discuss [2 marks]' but the scheme explicitly lists M1 (identify assumption) and M2 (explain breakdown/mechanism). This structure is appropriate for a 2-mark Discuss, but the scheme's own marker notes state 'do NOT award M2 without a physical mechanism', creating an implicit third criterion (physical mechanism justification) that blurs the boundary between the two marks. More problematically, Part (c) is marked as 'Comment on [3 marks]' with 3 bullets (fractional uncertainty calculation for method 1, for method 2, and overlap conclusion), which is acceptable. The dimensional mismatch occurs in Part (d): the Discuss rubric conflates 'explanation of how breakdown limits validity' with 'physical mechanism', and the marker notes enforce a gate on M2 that effectively requires M1 to be satisfied first—this is more like a 3-criterion rubric compressed into 2 marks.

FIX: For Part (d), either: (1) restructure as a 3-mark Discuss part with separate bullets for 'identifies assumption' / 'identifies physical mechanism of breakdown' / 'explains quantitative or qualitative limitation'; OR (2) if 2 marks must be retained, combine M1 and M2 into a single holistic criterion ('identifies an assumption and explains, with reference to a physical mechanism, how its breakdown limits validity'), and add a second bullet for a second valid assumption–mechanism pair, making it explicitly 2-answer-paths-to-2-marks. The current scheme risks ambiguity about whether M2 requires both identification AND mechanism justification simultaneously, violating the dimension's contract that each mark count matches the number of distinct operations.
topic pass

The ERQ authentically integrates both C.2 Wave model (primary) and A.1 Kinematics (secondary). C.2 is tested throughout (definitions, wave speed calculation via v=fλ, uncertainty analysis, Doppler-like scenario). A.1 Kinematics is genuinely required in (b)(ii)—the single-disturbance procedure demands kinematic distance/time analysis (v = d/t)—and is revisited in (d) where constant-velocity motion and the breakdown of kinematic assumptions underpin the discussion. The Doppler-type scenario explicitly invokes source kinematics. Neither topic is nominal; both drive the physics.

Planner output (stage 1)

Archetype: experimental setup
Scenario: A student uses a ripple tank to generate water waves with adjustable frequency and observes the wave pattern over a measured distance. The student measures the wavelength by marking successive wave crests and records the time for a single wave to travel across the tank. The experiment aims to determine the wave speed and verify the relationship between frequency, wavelength, and speed. A second part considers how the motion of the wave source itself would affect the observed frequency.
Cross-pollination part: d
Discriminator part: d

Part	Marks	AO	Command
a	2	AO1	Define
b(i)	3	AO2	Calculate
b(ii)	2	AO2	Determine
c	3	AO3	Explain
d	2	AO3	Evaluate

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