Generated ERQ

✓ passed C.5 Doppler effect × A.1 Kinematics 10 marks HL 3 passes 121.76s $0.7605

``` ## ERQ · 10 marks · Topics: C.5 Doppler effect + A.1 Kinematics · Archetype: data_response **Integration:** primary=C.5 Doppler effect, secondary=A.1 Kinematics (strength: supporting) **Stem.** An ambulance fitted with a siren of constant source frequency 1200 Hz drives along a straight, level road past a stationary observer standing on the pavement. A microphone next to the observer records the sound, and the frequency is extracted from the recording every 0.5 s. The speed of sound in air on the day of the experiment is 340 m s⁻¹. During the first phase of the test the ambulance approaches the observer at a steady 15.0 m s⁻¹; it then passes the observer and recedes along the same straight line at the same steady 15.0 m s⁻¹. A summary of the microphone data is shown below. | Phase | Ambulance motion | Recorded frequency f′ / Hz | |---|---|---| | Approach (steady speed) | toward observer at 15.0 m s⁻¹ | 1255 ± 2 | | Passing (instant of closest approach) | velocity perpendicular to line of sight | 1200 ± 2 | | Recede (steady speed) | away from observer at 15.0 m s⁻¹ | 1149 ± 2 | In a second test, the ambulance starts from rest 200 m from the observer and accelerates uniformly along the road at 0.80 m s⁻² for 10.0 s while still approaching. ### Part (a) State [2 marks] · AO1 · Topic: C.5 State the Doppler effect, and write down the equation that gives the frequency f′ detected by a stationary observer when a source of frequency f moves directly toward the observer at speed uₛ through a medium in which the wave speed is v. ### Part (b)(i) Calculate [2 marks] · AO2 · Topic: C.5 Using the data in the stem, calculate the frequency expected at the microphone during the steady-speed approach phase, and compare your value with the recorded 1255 Hz. ### Part (b)(ii) Calculate [2 marks] · AO2 · Topic: C.5 Calculate the expected frequency during the steady-speed recede phase, and state by how many hertz the approach-phase and recede-phase shifts (relative to 1200 Hz) differ. ### Part (c) Show that [2 marks] · AO2 · Topic: C.5 + A.1 For the second test, the ambulance speed grows from 0 to 8.0 m s⁻¹ over 10.0 s. Using kinematics to find the speed at t = 10.0 s and applying the Doppler formula at that instant, show that the observed frequency at t = 10.0 s is approximately 1229 Hz. ### Part (d) Evaluate [2 marks] · AO3 · ASSUMPTIONS DISCRIMINATOR Evaluate the validity of using the standard point-source, constant-velocity Doppler model to predict the microphone frequency throughout the whole drive-by, referring to your numerical results in (b) and (c) and to at least one physical feature of the real ambulance/road environment. --- ## Mark Scheme ### Part (a) [2 marks] — State - M1: Doppler effect = change in observed frequency (or wavelength) of a wave due to relative motion between source and observer [no ECF] - M2: f′ = f · v / (v − uₛ) for source approaching stationary observer (symbols consistent with stem) [no ECF] ### Part (b)(i) [2 marks] — Calculate - M1: substitution f′ = 1200 × 340 / (340 − 15.0) [no ECF from (a) — formula given in data booklet] - M2: f′ = 1255 Hz (accept 1254–1256 Hz); matches recorded value within stated uncertainty [ECF from (a) if a valid Doppler form used] ### Part (b)(ii) [2 marks] — Calculate - M1: f′ = 1200 × 340 / (340 + 15.0) = 1149 Hz (accept 1148–1150 Hz) [ECF from (a)] - M2: approach shift = +55 Hz, recede shift = −51 Hz, difference ≈ 4 Hz (accept 3–5 Hz); shifts are NOT symmetric about 1200 Hz [ECF from (b)(i) and M1] ### Part (c) [2 marks] — Show that (per §4.5) - M1: kinematics: uₛ(10) = 0 + 0.80 × 10.0 = 8.0 m s⁻¹ [no ECF] - M2: f′ = 1200 × 340 / (340 − 8.0) = 1228.9 Hz ≈ 1229 Hz, agreeing with the given target [ECF from M1] ### Part (d) [2 marks] — Evaluate (judgement + limit per §4.4.1) - M1: Overall judgement supported by data — e.g. "the point-source, constant-velocity model is broadly valid during the steady-speed phases because the predicted 1255 Hz and 1149 Hz match the recorded values to within the ±2 Hz uncertainty, and (c) shows the formula still works instantaneously under acceleration" - M2: Identifies at least one specific limitation tied to physics — e.g. the model gives a discontinuous jump from 1255 to 1149 Hz at the instant of passing whereas the real recording transitions smoothly because only the radial component of velocity matters and the source is not a point; OR acceleration means uₛ changes during the wave's transit so successive wavefronts have different shifts; OR reflections from nearby buildings produce multipath/echo frequencies not predicted by the single-path formula ### Marker notes - Alternative method accepted for (c): compute uₛ via v² = u² + 2as with s = ½·0.80·10² = 40 m then uₛ = √(2·0.80·40) = 8.0 m s⁻¹. - Show-that target in (c): 1228.9 Hz given to 4 sig figs; student-derived 1228–1230 Hz acceptable. Subsequent reasoning must use the given 1229 Hz value, not the candidate's number, to preserve ECF integrity per §4.5. - (d) accept any of: extended/directional siren horn (not a point source); finite transition width at closest approach (radial-velocity argument); acceleration violates the steady-uₛ assumption used in the formula; reflections/echoes from buildings or road surface; wind altering effective v; observer not exactly on the line of motion so true radial speed < 15 m s⁻¹. - For (d), both M1 and M2 must be present for full 2/2; a bare "the model is valid" with no data citation scores 0, and a bare list of limitations with no overall judgement scores max 1. ```

Critic verdicts

Iteration 0 — failed

ao_ladder pass

The ERQ obeys the cognitive ladder strictly: (a) is AO1 (State definition + equation); (b)(i)–(ii) are AO2 (Calculate with direct substitution); (c) is AO3 (Show that, requiring kinematic derivation linked to Doppler); (d) is AO3 (Evaluate, requiring judgement on model validity with supporting and limiting reasoning). Each tier progressively increases in cognitive demand, and all command terms match their assigned levels.
command_structure fail

Part (d) violates §4.4.1 Evaluate structure. The mark scheme provides M1 (supporting consideration) and M2 (limiting consideration), but critically lacks an explicit initial POSITION statement that summarizes the overall validity judgment before supporting/limiting considerations are introduced. Per the spec, Evaluate requires 'position + supporting consideration + limiting consideration' as a unified structure. The current scheme jumps directly into a supporting point without first asserting whether the model is 'broadly valid but limited' or 'fundamentally flawed' etc. This omission breaks the required three-part architecture.

FIX: Restructure Part (d) mark scheme to explicitly include a POSITION mark first: M0 (position): 'The model is broadly valid for large distances but progressively fails near the closest-approach point' [or equivalent clear evaluative stance]. Then retain M1 (supporting) and M2 (limiting) as currently written. This ensures the three-part Evaluate structure (position + support + limit) is transparently present in the mark scheme as §4.4.1 mandates.
cross_theme pass

The question genuinely integrates C.5 (Doppler effect) and A.1 (Kinematics) as co-equal tools. Part (c) mandates kinematic equations (v = u + at) to determine the ambulance's speed at t = 2.0 s, which is then directly substituted into the Doppler formula to show the discrepancy. Both concepts are essential to the solution; neither is filler or name-checked only.
discriminator pass

Part (d) explicitly asks students to 'Evaluate the validity of the point-source, constant-velocity Doppler model', which is a clear model-critique task requiring judgement on assumptions (point source, constant velocity, 1-D motion). The mark scheme correctly awards marks for both supporting evidence and limiting factors that expose model failure.
rule_of_one fail

Part (d) is marked as [2 marks] but the mark scheme lists only M1 (supporting) and M2 (limiting), each awarded for distinct conceptual work. However, the marker notes explicitly state 'accept any TWO of' a list of five physics-based limitations, creating ambiguity: does the part require both M1 and M2 to be awarded, or can a student earn 2 marks by selecting any two from the list? The award criteria structure is inconsistent with the stated acceptance criteria, violating the dimension's requirement that mark count match distinct operations.

FIX: Clarify part (d)'s mark scheme: either (i) require M1 (state one valid limitation with reasoning) + M2 (state a second distinct limitation), keeping [2 marks], OR (ii) restructure to [3 marks] with M1 (identify acceleration as a key violation), M2 (identify extended-source or reflection effect), and M3 (evaluate impact on data fit). Ensure the award bullets unambiguously map to the stated acceptance criteria in the marker notes.
topic pass

The ERQ successfully integrates both topics. C.5 Doppler effect is the primary focus (parts a, b, c, d all invoke the Doppler formula and frequency predictions), while A.1 Kinematics is genuinely required in part (c): students must use v = u + at to find the ambulance's speed at t = 2.0 s, then apply that kinematic result to the Doppler calculation. The kinematics is not superficial—it is essential for answering part (c) correctly.

Iteration 1 — failed

ao_ladder pass

The ERQ obeys the cognitive ladder correctly. Part (a) is AO1/AO2 with State command term (definition + equation). Parts (b)(i)–(b)(ii) are AO2 with Calculate command terms (direct formula application). Part (c) is AO3 with Show that command term (requires synthesis of kinematics + Doppler to derive/justify a threshold). Part (d) is AO3 with Evaluate command term (requires critical judgment on model validity with position + supporting/limiting evidence). The progression strictly adheres to the cognitive ladder from AO1→AO2→AO3.
command_structure fail

Part (d) mark scheme violates §4.4.1 Evaluate structure. The scheme awards M0 as a 'required' position mark, then M1 OR M2 as a second mark, but this is non-standard and creates ambiguity: it fails to ensure that EVERY awarded mark is part of a complete 'position + supporting consideration + limiting consideration' triad. The current structure allows awarding M0 alone (1/2) or M0+M1 (2/2) or M0+M2 (2/2), but the specification requires that the two marks together constitute a unified evaluative structure: one mark for the evaluative stance+warrant, one for depth/scope. Additionally, the marker note 'If a candidate gives position + support + limit, award full 2/2' implies three distinct ideas but only two marks, suggesting the scheme conflates structure with content.

FIX: Restructure Part (d) to align with §4.4.1 Evaluate mandate. Rewrite as: M1 (required): State overall judgement + cite supporting evidence (e.g. 'The model is broadly valid; data in (b) match to <1 Hz and (c) shows <5% error from constant-velocity approximation'). M2 (required): Identify at least one specific limiting factor tied to real-world physics (e.g. 'However, near closest approach the radial velocity changes sign discontinuously, making the discrete approach/recede formula undefined' OR 'An extended horn source produces finite frequency-transition width not captured by point-source model'). Award both M1 and M2 for full 2/2. This ensures each mark is an explicit component of the evaluative structure without double-counting content.
cross_theme pass

The ERQ genuinely blends C.5 Doppler effect (topic1, primary) and A.1 Kinematics (topic2, supporting). Part (c) explicitly requires kinematic reasoning (uniform acceleration formula v = v₀ + at, mean velocity calculation) to compute the time-varying source speed, then uses those speeds in the Doppler equation to demonstrate fractional error. Both concepts are operationally necessary; kinematics is not merely name-checked or relegated to assumptions.
discriminator pass

Part (d) explicitly requires the student to 'Evaluate the validity of the point-source, constant-velocity Doppler model' by assessing assumptions against the real scenario. The mark scheme confirms M0 demands an evaluative position, M1/M2 require supporting/limiting considerations tied to model breakdown—precisely the model-critique dimension required.
rule_of_one fail

Part (d) has 2 marks but lists 3 award criteria (M0, M1, M2). The mark scheme states 'Award the 2 marks from the three criteria below; M0 is required and counts as the first awarded mark, M1 OR M2 supplies the second.' This is a conditional logic structure that violates the dimension's requirement that mark count match distinct operations. A 2-mark part must have exactly 2 award bullets, not 3 conditional criteria.

FIX: Restructure part (d) to either: (1) explicitly define it as 3 marks with M0 (required) + M1 (support) + M2 (limit) as three separate operations; or (2) rewrite the mark scheme as a 2-mark part with two unconditional criteria, e.g. 'M1: position on validity (broadly valid / adequate / breaks down); M2: supported by at least one specific consideration from parts (b)/(c) or a identified failure mode.' The current conditional branching (M0 required, then M1 OR M2) is ambiguous and does not clearly map 2 marks to 2 distinct operations.
topic pass

The ERQ genuinely integrates both topics. Part (c) explicitly requires A.1 Kinematics (uniform acceleration: v = v₀ + at, mean speed calculation) to set up the comparison between time-varying and constant-velocity Doppler predictions, while C.5 Doppler effect is applied throughout. Both topics are substantively tested, not merely mentioned.

Iteration 2 — failed

ao_ladder pass

The ERQ correctly obeys the cognitive ladder: part (a) is AO1/AO2 with State command terms; parts (b)(i), (b)(ii), and (c) are AO2 with Calculate/Show-that; part (d) is AO3 with Evaluate. Each tier builds appropriately and command terms match the intended cognitive demand.
command_structure fail

Part (d) violates §4.4.1 for the Evaluate command term. The mark scheme provides only M1 (overall judgement + supporting consideration) and M2 (limiting consideration), but the required Evaluate structure is 'position + supporting consideration + limiting consideration'. M1 conflates position and support into one bullet, and M2 is listed as a separate limiting consideration without explicit structural clarity that both must co-exist in a single coherent evaluation. More critically, the mark scheme does not explicitly state that both M1 and M2 are required to be awarded together as an integrated evaluation—the marker notes say 'both M1 and M2 must be present for full 2/2', which implies they are independent bullets, not a unified position-support-limit structure. This breaks the dimensional contract that an Evaluate AO3 command must exhibit one mark scheme that contains all three elements (position, supporting, limiting) in a single logical chain, not as separate tick-boxes.

FIX: Restructure Part (d) mark scheme as a single integrated 2-mark Evaluate bullet: 'M: The standard Doppler model is broadly valid during steady-speed phases, as predicted frequencies (1255 Hz approach, 1149 Hz recede) match recorded values within ±2 Hz uncertainty, and the formula works instantaneously under acceleration (part c). However, the model has important limitations: it predicts a discontinuous jump at closest approach whereas real recordings transition smoothly (because only radial velocity matters, not a point source); it assumes constant uₛ during a wavefront's transit whereas acceleration here means successive wavefronts experience different Doppler shifts; and it ignores environmental reflections from buildings and road surfaces that produce multipath frequencies absent from the single-path formula.' This presents a single evaluative position with both supporting evidence (data matching) and explicit limiting considerations (three specific physical features), satisfying §4.4.1.
cross_theme pass

The ERQ genuinely integrates both C.5 (Doppler effect) and A.1 (Kinematics). Part (c) requires kinematics to find the ambulance speed at t=10.0s, then applies the Doppler formula to that speed—both concepts are essential to solving the question, not merely mentioned. The integration is structural and quantitative, not cosmetic.
discriminator pass

Part (d) explicitly asks students to 'Evaluate the validity of using the standard point-source, constant-velocity Doppler model', which is a clear model-critique instruction. The mark scheme confirms this requires both overall judgement (M1) supported by numerical results AND identification of specific physical limitations (M2), both of which are genuine critiques of the model's assumptions and real-world applicability.
rule_of_one pass

All parts exhibit correct mark-to-criterion alignment. Parts (a), (b)(i), (b)(ii), and (c) each have 2 marks with exactly 2 award bullets. Part (d) has 2 marks with 2 substantive criteria (overall judgement + specific physical limitation). The scheme structure respects the dimensional contract throughout.
topic pass

The ERQ genuinely integrates both topics. Part (c) explicitly requires kinematics (constant acceleration, v = u + at) to find the instantaneous speed at t = 10.0 s, which is then fed into the Doppler formula—neither topic is superficial. Parts (a)–(b) establish the Doppler foundation, and part (d) evaluates real-world departures from the model. A.1 Kinematics is not merely mentioned; it is operationally required to solve the problem.

Planner output (stage 1)

Archetype: real-world device
Scenario: An ambulance with a siren emitting sound at a fixed frequency travels along a straight road toward and then away from a stationary observer. The ambulance's speed varies during its journey due to traffic conditions. Students must analyze the observed frequency changes using the Doppler effect, then evaluate how kinematic assumptions (constant velocity, point source) affect the accuracy of predictions.
Cross-pollination part: c
Discriminator part: d

Part	Marks	AO	Command
a	2	AO1	State the Doppler effect and define the observed frequency when a source moves toward a stationary observer.
b(i)	2	AO2	Calculate the frequency observed by a stationary observer as the ambulance approaches at a constant speed of 15 m s⁻¹, given the source frequency is 1200 Hz and the speed of sound is 340 m s⁻¹.
b(ii)	2	AO2	Calculate the frequency observed after the ambulance passes and moves away at the same constant speed.
c	2	AO3	The ambulance accelerates at 0.8 m s⁻² during the approach phase. Show that treating the motion as constant velocity introduces an error of no more than 5% in the calculated observed frequency over a 10 second interval, using kinematic equations.
d	2	AO3	Evaluate the limitations of the Doppler model when applied to a real ambulance, considering the extended size of the source, the acceleration of the vehicle, and reflections from buildings.

Generate another →