Generated ERQ

✓ passed C.5 Doppler effect × A.1 Kinematics 10 marks SL 3 passes 106.69s $0.6056

## ERQ · 10 marks · Topics: C.5 Doppler effect + A.1 Kinematics **Stem.** A physics student stands on a straight, level pavement and records the siren of an approaching ambulance using a smartphone spectrum-analyser app. The ambulance siren emits a single tone at a source frequency of 800 Hz. As the vehicle approaches in a straight line along the road at constant speed, the app displays a steady received frequency of 850 Hz. After the ambulance passes the student and recedes along the same road, the app displays a steady received frequency of 760 Hz. The speed of sound in air on this day is 340 m s⁻¹. The student assumes the ambulance maintains constant velocity throughout, and that the line of sight from observer to source lies along the direction of motion. ### Part (a) State [2 marks] · AO1 · Topic: C.5 State the equation for the frequency f′ detected by a stationary observer when a sound source of frequency f moves directly toward the observer at speed uₛ through a medium in which sound travels at speed v, and define each symbol. ### Part (b)(i) Calculate [3 marks] · AO2/AO3 · Topic: C.5 Using the approach data (f′ = 850 Hz), calculate the speed of the ambulance. ### Part (b)(ii) Calculate [2 marks] · AO2/AO3 · Topic: C.5 Using the recession data (f′ = 760 Hz), calculate the speed of the ambulance. ### Part (c) Evaluate [2 marks] · AO3 · Topic: C.5+A.1 The student notes that the ambulance moves between the two measurements over a time interval of 4.0 s. Treating the two speeds from (b)(i) and (b)(ii) as the instantaneous speeds before and after passing, calculate the average acceleration of the ambulance and comment on whether the assumption of constant velocity is justified. ### Part (d) Suggest [1 mark] · AO3 · ASSUMPTIONS DISCRIMINATOR Suggest one reason why the two speeds calculated in (b)(i) and (b)(ii) might differ even if the ambulance's true road speed were genuinely constant. --- ## Mark Scheme ### Part (a) [2 marks] - Mark 1: equation stated as f′ = f · v / (v − uₛ) [ECF: no] - Mark 2: symbols defined — v = speed of sound in medium; uₛ = speed of source; f = emitted (source) frequency; f′ = observed frequency (at least three of four defined correctly) [ECF: no] ### Part (b)(i) [3 marks] - Mark 1: rearrangement uₛ = v(1 − f/f′) OR equivalent algebraic isolation of uₛ from f′ = fv/(v − uₛ) [ECF: no] - Mark 2: substitution uₛ = 340 × (1 − 800/850) OR uₛ = 340 − (800 × 340)/850 [ECF: yes from a] - Mark 3: uₛ = 20 m s⁻¹ (accept 20.0 m s⁻¹; 2 s.f. minimum, correct units) [ECF: yes] ### Part (b)(ii) [2 marks] - Mark 1: correct recession formula and substitution: uₛ = v(f/f′ − 1) = 340 × (800/760 − 1) [ECF: yes from a] - Mark 2: uₛ = 17.9 m s⁻¹ ≈ 18 m s⁻¹ (correct units, 2 s.f.) [ECF: yes] ### Part (c) [2 marks] - Mark 1: average acceleration computed as a = Δu/Δt = (17.9 − 20)/4.0 = −0.53 m s⁻² (accept −0.5 m s⁻² to −0.55 m s⁻²; negative sign or "deceleration" required) [ECF: yes from b(i) and b(ii)] - Mark 2: comment that the speed change is small / the assumption of constant velocity is approximately justified BUT not exact, since a non-zero acceleration is detected (must reference the numerical value AND make a judgement) [ECF: yes] ### Part (d) [1 mark] - Mark 1: any ONE valid physical reason, e.g.: - the ambulance's velocity is not exactly along the line of sight to the observer (transverse/angular component), so only the radial component contributes to the Doppler shift; - wind / motion of the air medium alters the effective speed of sound between approach and recession; - the driver genuinely decelerated slightly between passing and the recession measurement; - measurement uncertainty in the spectrum-analyser app / frequency resolution. [ECF: no] ### Marker notes - Part (b)(i)/(ii): accept the alternative low-velocity approximation Δf/f ≈ uₛ/v giving uₛ = 21.25 m s⁻¹ and 17.0 m s⁻¹ respectively for full marks, provided the approximation is stated. - Part (c): if a candidate uses the approximation values from the marker note above, accept a = (17.0 − 21.25)/4.0 = −1.06 m s⁻² with appropriate ECF. - Part (c) Mark 2: do NOT award if the candidate only states "yes, constant" or "no, not constant" without reference to the calculated acceleration magnitude. - Part (d): do NOT accept "human error" or vague "the formula is wrong" without identifying a specific physical mechanism.

Critic verdicts

Iteration 0 — failed

ao_ladder fail

The cognitive ladder is broken. Part (b)(i) and (b)(ii) are both marked as AO2/AO3 with 'Calculate' command terms, but they should be tiered differently. Part (c) uses 'Determine' (AO2/AO3) when it should be AO3 with 'Explain/Evaluate' for the constant-velocity judgment. Part (d) correctly uses 'Suggest' (AO3), but the middle tier lacks clear progression.

FIX: Restructure as follows: (a) State [2 marks] AO1 ✓; (b)(i) Calculate [2 marks] AO2 (approach speed only); (b)(ii) Calculate [2 marks] AO2 (recession speed only); (c) Evaluate [3 marks] AO3 (compare speeds, calculate acceleration, and explain whether constant-velocity assumption is valid); (d) Suggest [1 mark] AO3 ✓. This creates a proper AO1→AO2→AO2→AO3→AO3 ladder with command-term progression and clearer cognitive discrimination.
cross_theme fail

Part (c) invokes A.1 kinematics (acceleration = Δv/Δt) only as a calculation procedure, not as a genuine blended concept. The Doppler effect could be solved without kinematics by simply stating the speeds differ. Part (d) is a separate assumptions discriminator that does not integrate kinematics into the physics reasoning. The two topics do not jointly solve the problem.

FIX: Restructure the question so kinematics genuinely contributes to the Doppler analysis. For example: (c) could ask students to assume constant acceleration and derive the instantaneous velocity at closest approach using v = (v_approach + v_recession)/2 or kinematics equations, then verify whether this instantaneous speed is consistent with the time-averaged Doppler shift. Alternatively, ask students to model the ambulance motion using kinematic equations (s = ut + ½at²) and show how the changing velocity during the 0.40 s transition window affects the expected frequency profile over time, requiring them to integrate both Doppler and kinematic reasoning to explain the measured frequencies.
discriminator pass

Part (d) explicitly requires the student to suggest a physical reason why the measured frequencies differ from the true road speed when the Doppler formula is applied — a direct model-critique task. The mark scheme accepts multiple valid critiques (oblique geometry, wind, echoes, non-point source, measurement geometry), all of which address assumptions or limitations of the idealized 1-D Doppler model.
rule_of_one fail

Part (b)(ii) declares 2 marks but lists only 1 distinct award criterion (formula + substitution combined in a single bullet). The calculation part should explicitly separate: (1) formula/rearrangement, (2) substitution with values, (3) numerical answer with units. Currently only 1 bullet exists where 2 are claimed.

FIX: Split part (b)(ii) Mark 1 into two separate bullets: Mark 1 for 'Uses receding form f′ = f · v / (v + uₛ) → uₛ = v(f/f′ − 1)' and Mark 2 for 'Substitution: uₛ = 340 × (800/760 − 1)'. Then add Mark 3 for 'uₛ = 17.9 m s⁻¹ (accept 18 m s⁻¹) with units, 2–3 s.f.' This makes (b)(ii) a 3-mark Calculate part with 3 distinct operations, matching part (b)(i). Alternatively, reduce (b)(ii) to 1 mark if only the final answer is awarded.
topic pass

The ERQ genuinely integrates both topics. C.5 (Doppler effect) is the primary physics content in parts (a)–(d), with repeated application of the Doppler formula for approach and recession. A.1 (Kinematics) is authentically invoked in part (c), where students must use the kinematic equation a = Δu/Δt to compute acceleration from the two speeds and the transition time, then reason about constant-velocity assumptions. Neither topic is merely nominal; both are operationally necessary to complete the question.

Iteration 1 — failed

ao_ladder pass

The ERQ obeys the cognitive ladder correctly: (a) is AO1 with State command; (b)(i)–(ii) are AO2 with Calculate commands; (c) is AO3 with Evaluate command requiring both calculation and reasoned physical judgement; (d) is AO3 with Suggest command requiring discrimination of assumptions. The progression from recall → application → evaluation is proper and well-sequenced.
cross_theme pass

Part (c) genuinely blends both topics: Doppler effect (C.5) is used to extract the line-of-sight velocities from the frequency shifts, and kinematics (A.1) is used to calculate acceleration from the change in velocity over time and to interpret the result physically. The kinematic analysis is not merely name-checked—it is central to the solution and evaluation. Part (d), while somewhat tangential, does not undermine the core blending in (c).
discriminator pass

Part (d) explicitly asks the student to 'Suggest one reason, other than the geometry effect in (c), why the frequency measured by the microphone in a real urban recording would differ from the value predicted by the Doppler formula.' This is a clear model-critique dimension: it requires identification of a limitation or assumption failure (wind, reflections, absorption, microphone motion, non-pure tone, temperature gradients) that would cause real data to deviate from the idealized Doppler prediction. The mark scheme confirms this with specific physical mechanisms accepted and vague answers rejected.
rule_of_one fail

Part (c) is marked out of 3 but contains 4 distinct award criteria: (1) compute Δv, (2) apply a = Δv/Δt, (3) evaluate plausibility and reject literal braking, and (4) implicitly explain the geometric (angle) mechanism. The mark scheme lists 3 bullets but the third bullet conflates two separate operations (numerical calculation of acceleration + reasoned evaluation requiring understanding of geometry). This violates the dimension requirement that a 3-mark Calculate/Evaluate part have exactly 3 award criteria matching the 3 marks.

FIX: Restructure Part (c) as follows: Mark 1 = compute Δv; Mark 2 = calculate a = Δv/Δt; Mark 3 = provide a single unified award criterion that awards full credit only if the candidate *both* calculates a ≈ 9.5 m s⁻² *and* explains that this magnitude is implausible for sustained braking, *and* correctly identifies that the apparent velocity change arises from the changing line-of-sight projection angle (geometry), not from actual vehicle deceleration. Alternatively, split Part (c) into two subparts: (c)(i) [2 marks] Calculate acceleration; (c)(ii) [1 mark] Evaluate plausibility and explain geometry. This brings the structure into alignment with the mark count.
topic pass

The ERQ genuinely integrates both topics. Part (c)—the core evaluative section—explicitly requires kinematics (uniform acceleration equation a = Δv/Δt) applied to the velocity component data derived from Doppler calculations, and crucially demands physical reasoning about whether the acceleration is consistent with actual braking or instead arises from geometric line-of-sight projection. Both C.5 and A.1 concepts are essential, not nominal.

Iteration 2 — failed

ao_ladder pass

The ERQ correctly obeys the cognitive ladder: Part (a) is AO1 (State definition); parts (b)(i)–(b)(ii) are AO2/AO3 (Calculate); part (c) is AO3 (Evaluate with numerical reasoning and judgement); part (d) is AO3 (Suggest with physical reasoning). Command terms align precisely with cognitive demand at each tier.
cross_theme fail

Part (c) is labeled as blending C.5 + A.1, but kinematics is only superficially invoked to calculate acceleration from two speeds. The question does not genuinely require kinematics concepts (displacement, velocity-time relationships, or motion analysis) to be integrated into the solution; it merely applies the kinematic definition a = Δv/Δt as a final arithmetic step. A.1 is not truly woven into the Doppler physics—it appears only as a mechanical post-calculation, not as a genuine conceptual blend where both frameworks inform the physical reasoning.

FIX: Restructure part (c) to require students to use kinematic equations more substantially. For example: 'The student estimates the ambulance travelled 74 m between the two measurements. Using the two calculated speeds as initial and final velocities, determine the constant acceleration required and the average speed. Compare this with the instantaneous speeds and comment on the validity of the constant-velocity assumption.' This forces genuine integration of A.1 (kinematic equations of motion) with C.5 (Doppler-derived speeds) rather than treating kinematics as mere housekeeping.
discriminator fail

Part (d) asks students to 'suggest one reason why the two speeds might differ,' which is a critique of the model's assumptions (questioning whether constant velocity was truly maintained or identifying physical factors affecting measurements). However, this is a single 1-mark question that only asks for ONE suggestion—it does not constitute a substantial final part that 'discusses' or 'explains' a limitation in depth as the dimension requires. The ERQ lacks a comprehensive concluding part that critically evaluates the model assumptions at length.

FIX: Expand part (d) to a 2–3 mark question requiring students to discuss multiple assumptions or more fully explain limitations—e.g., 'Discuss two reasons why the calculated speeds differ and how each assumption in the Doppler model may have been violated' or 'Explain why treating the ambulance's motion as purely radial is a limitation of this model.' Alternatively, add a part (e) that asks students to critique the constant-velocity assumption or discuss how wind/medium motion affects the measured Doppler shifts in detail.
rule_of_one fail

Part (b)(ii) mark count (2 marks) does not match the number of distinct operations listed (1 formula/substitution + 1 answer = 2 marks). However, the structure is acceptable. The critical failure is Part (c): it is labeled as a 2-mark part but the mark scheme lists only 2 awards, yet one of those awards (Mark 2) requires TWO distinct cognitive operations: (1) numerical calculation of acceleration AND (2) a substantive evaluative comment linking the result to the constant-velocity assumption. A 2-mark Calculate/Evaluate part should have at most 2 independent award bullets; instead, Mark 2 conflates calculation verification with evaluative reasoning, creating ambiguity about whether partial credit (1 mark) is awarded for correct acceleration alone without the comment.

FIX: Restructure Part (c) as a 3-mark part: Mark 1 = correct rearrangement/formula for a; Mark 2 = correct substitution and numerical answer for acceleration; Mark 3 = valid evaluative comment on the constant-velocity assumption with reference to the magnitude. Alternatively, if keeping 2 marks, split Mark 2 into (i) acceleration value and (ii) comment as distinct sub-bullets with clear guidance on when each is awarded. Clarify in the marker notes whether 1 mark is possible if only the acceleration is correct but no evaluative comment is given.
topic pass

The ERQ substantively tests both C.5 (Doppler effect) and A.1 (Kinematics). Parts (a)–(b) focus on the Doppler formula and calculating source speeds from frequency shifts. Part (c) explicitly requires kinematic analysis: computing Δu/Δt to find acceleration over a time interval, which is the core A.1 concept. The two topics are genuinely integrated in part (c), not merely nominally mentioned—the student must apply both the Doppler results and kinematic equations to evaluate the constant-velocity assumption. Part (d) adds critical thinking about assumptions without diluting the dual-topic requirement.

Planner output (stage 1)

Archetype: real-world device
Scenario: An ambulance siren emits sound at a fixed frequency while moving toward and then away from a stationary observer. The observer measures the heard frequency using a smartphone app. Students must relate the observed frequency shift to the ambulance's velocity, apply kinematic reasoning to infer motion parameters, and evaluate the limitations of assuming constant velocity during the siren's approach and recession.
Cross-pollination part: c
Discriminator part: d

Part	Marks	AO	Command
a	2	AO1	State the relationship between observed frequency, source frequency, and velocity for a moving source
b(i)	3	AO2	Calculate the frequency heard by the observer when the ambulance approaches at 20 m s⁻¹, given source frequency 800 Hz and speed of sound 340 m s⁻¹
b(ii)	2	AO2	Calculate the frequency heard when the ambulance recedes at the same speed
c	2	AO3	The observer measures a frequency shift of 180 Hz as the ambulance passes. Using kinematic analysis, determine whether the ambulance's speed is constant and explain any discrepancy from the assumed 20 m s⁻¹
d	1	AO3	Suggest one physical effect not accounted for in the Doppler formula that would modify the observed frequency in a real urban environment

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