These are original Marlbridge practice questions, not past exam questions. The mark points are a suggested Marlbridge rubric to help you check your work; they are not an official scoring guideline. Data and assumptions for every question: the speed of sound in still air is 340 m/s; all speeds are constant and well below the wave speed; f₀ is the rest frequency of a source and f is the frequency an observer measures. The Doppler effect is treated qualitatively. Any calculation uses only v = fλ.
Question 1 (multiple choice · foundation)
A delivery van sounds its horn continuously while driving straight toward a pedestrian at constant speed. The pedestrian stands still. Which statement describes what the pedestrian hears while the van approaches?
- (A) A pitch higher than the horn’s rest pitch, rising steadily as the van gets closer
- (B) A constant pitch higher than the horn’s rest pitch, getting louder
- (C) The horn’s rest pitch, getting louder
- (D) A constant pitch lower than the horn’s rest pitch, getting louder
Answer and explanation
Answer: (B). The separation shrinks at a constant rate, so every crest has a shorter trip than the one before by the same amount. The crests arrive at a constant rate that is higher than f₀. The amplitude reaching the pedestrian grows as the van gets nearer, so the sound gets louder.
- (A) confuses loudness with pitch. At constant velocity the frequency does not keep rising.
- (C) ignores the Doppler effect. Relative motion toward the listener raises f.
- (D) has the direction wrong. A lower pitch is heard when the van moves away.
Question 2 (multiple choice · core)
A small drone carries a speaker that emits a steady tone. Four microphones record it:
- Mic 1 is fixed to a post; the drone flies directly toward it at 12 m/s.
- Mic 2 is fixed to a post; the drone flies directly away from it at 12 m/s.
- Mic 3 hangs from a second drone that flies beside the first with the same velocity.
- Mic 4 is fixed to a post; the drone flies directly toward it at 6 m/s.
Which ranking of the recorded frequencies, from highest to lowest, is correct?
- (A) Mic 1 > Mic 4 > Mic 3 > Mic 2
- (B) Mic 4 > Mic 1 > Mic 3 > Mic 2
- (C) Mic 1 = Mic 4 > Mic 3 > Mic 2
- (D) Mic 1 > Mic 4 > Mic 2 > Mic 3
Answer and explanation
Answer: (A). Mics 1 and 4 have the separation shrinking, so f > f₀; the faster approach (12 m/s) gives the larger shift, so Mic 1 is highest. Mic 3 moves with the drone, so the separation is constant and f = f₀. Mic 2 has the separation growing, so f < f₀.
- (B) reverses the size rule. A greater relative speed gives a greater shift, not a smaller one.
- (C) treats any approach as giving the same shift. The direction sets the sign, but the speed sets the size.
- (D) places Mic 3 lowest, as if moving with the source lowered the frequency. With no change in separation there is no shift.
Question 3 (multiple choice · core)
A spectral line from a distant star is measured at a slightly longer wavelength than the same line produced in a laboratory at rest. What can you conclude?
- (A) The star is moving toward Earth.
- (B) The star is moving away from Earth.
- (C) The star’s light is travelling more slowly than light from the laboratory source.
- (D) Nothing, because light needs no medium, so it cannot show a Doppler shift.
Answer and explanation
Answer: (B). A longer observed wavelength means a lower observed frequency (red shift). For light, a lower observed frequency means the source and observer are moving apart.
- (A) is the blue-shift case: approaching gives a shorter wavelength.
- (C) is wrong because light in a vacuum always travels at c = 3.00 × 10⁸ m/s. The shift is in wavelength and frequency, not speed.
- (D) is wrong because the Doppler effect depends on relative velocity. Light does not need a medium for that.
Question 4 (multiple choice · core)
A radar speed gun sends out radio waves of a fixed frequency. The waves reflect off a car and return to the gun. The car drives directly away from the gun. How does the frequency of the returning waves compare with the frequency sent out, and how does that change if the car goes faster?
- (A) Lower; the difference gets larger if the car goes faster.
- (B) Higher; the difference gets larger if the car goes faster.
- (C) Lower; the difference does not depend on the car’s speed.
- (D) The same, because the gun itself is not moving.
Answer and explanation
Answer: (A). The car is moving away from the gun, so the waves reach the car at a lower frequency than they were sent. The car then acts as a receding source of the reflected waves, so the gun receives an even lower frequency. A greater relative speed gives a greater shift.
- (B) gives the result for a car approaching the gun.
- (C) ignores the size rule: the shift grows with the relative speed. That is how the gun measures speed.
- (D) forgets that relative motion is what matters, and the car moves relative to the gun.
Question 5 (calculation · core)
In a ripple tank, a small dipper vibrates up and down while moving steadily across the water. A photograph shows that the crests on one side of the dipper are 1.2 cm apart and the crests on the other side are 1.8 cm apart. Water waves in this tank travel at 24 cm/s.
(a) On which side of the dipper is it moving: toward the 1.2 cm crests or toward the 1.8 cm crests? Explain. (b) Calculate the frequency at which crests pass a float fixed on each side. (c) Explain why the dipper’s own frequency must lie between your answers to (b). Then find it, given that the motion shortens the spacing on one side by the same amount it lengthens it on the other.
Worked solution and suggested Marlbridge rubric
(a) The dipper moves toward the 1.2 cm crests. Each new crest is emitted a little further along in the direction of motion, so the crests are squeezed together ahead of the dipper and spread out behind it.
(b) The wave speed is set by the water, so v = 24 cm/s on both sides. Ahead: f = v/λ = 24 ÷ 1.2 = 20 Hz. Behind: f = 24 ÷ 1.8 = 13.3 Hz (13.33 Hz).
(c) The float ahead has the separation shrinking, so it sees f above the rest frequency; the float behind sees f below it. So 13.3 Hz < f₀ < 20 Hz. The rest spacing is the average of the two spacings: (1.2 + 1.8)/2 = 1.5 cm. So f₀ = 24 ÷ 1.5 = 16 Hz, which does lie between 13.3 Hz and 20 Hz. Part (c) is extra practice with v = fλ: the exam treats the Doppler effect qualitatively and will not ask you to calculate a shift.
| Point | What earns it |
|---|---|
| 1 | Moving toward the 1.2 cm crests, because crests bunch up in the direction of motion |
| 1 | Uses v = fλ with the same wave speed on both sides |
| 1 | 20 Hz and 13.3 Hz, each with unit |
| 1 | Explains that the approached side is above f₀ and the other side below it, so f₀ lies between them |
| 1 | Rest spacing 1.5 cm and f₀ = 16 Hz |
Common error: assuming the waves travel faster in front of the dipper. Source motion changes the spacing, not the wave speed.
Question 6 (constructed response · core)
A train sounds its horn continuously as it passes along a straight track at constant speed. A student stands on the platform, a few metres from the track, and records the frequency she hears from when the train is far away and approaching until it is far away and receding.
(a) Sketch a graph of observed frequency f against time t. Mark the rest frequency f₀ as a dashed horizontal line and label the moment the train passes. (b) Explain the shape of your graph. (c) A second, faster train with an identical horn passes in the same way. On the same axes, sketch its graph and justify two differences.
Worked solution and suggested Marlbridge rubric
(a) The graph starts as a nearly flat line above f₀, falls smoothly and quite steeply around the moment of passing, crossing f₀ near that moment, and ends as a nearly flat line below f₀.
(b) Far away and approaching, the train moves almost directly toward the student, so the separation shrinks at almost the train’s full speed: a steady f above f₀. Near the platform, the train’s motion turns from toward her, to across her line of sight, to away from her, so the separation’s rate of change falls to zero and reverses. The sound emitted when the train is moving across her line of sight arrives at f₀. Far away and receding, the separation grows at almost the full speed: a steady f below f₀.
(c) The faster train’s graph starts higher above f₀ and ends lower below f₀, because a greater relative speed gives a greater shift. Its drop also happens over a shorter time, because the faster train turns from approaching to receding more quickly. It still crosses f₀ near the moment of passing.
| Point | What earns it |
|---|---|
| 1 | Sketch: flat above f₀, falling through f₀ near passing, flat below f₀ (no rise before passing) |
| 1 | Explains the high and low values from shrinking and growing separation |
| 1 | Explains the fall in terms of the changing direction of the train’s motion relative to the line of sight |
| 1 | Faster train: higher starting value and lower final value, linked to greater relative speed |
| 1 | Faster train: drop over a shorter time, with a reason |
Do not award the first point for a graph that rises as the train approaches.
Question 7 (constructed response · stretch)
A ferry moves across a calm lake at constant velocity. A buzzer is fixed at the back (stern) of the ferry, and a passenger stands at the front (bow). A light, steady wind blows over the lake. A friend waits on a jetty straight ahead of the ferry.
A student claims: “The passenger at the bow hears a lower frequency than the buzzer’s rest frequency, because the sound waves have to chase the bow, which is moving away from them.”
(a) Evaluate the student’s claim. Use an argument about the times at which successive crests arrive. (b) Compare the frequency heard by the friend on the jetty with the buzzer’s rest frequency. Justify your answer. (c) The ferry speeds up to a new constant velocity. State and explain any change in what the passenger and the friend hear.
Worked solution and suggested Marlbridge rubric
(a) The claim is wrong. The buzzer and the passenger move with the same velocity, so the distance between them is constant. The buzzer emits one crest every period T₀. Every crest starts at the buzzer and must reach a bow that is always the same distance ahead of it, in the same steady conditions. So every crest makes an identical trip and takes the same time to arrive. The crests therefore arrive T₀ apart, and the passenger hears f = f₀. The bow does move away from where each crest was emitted, but it does so equally for every crest. A steady wind changes all the trip times equally, so it does not change this.
(b) The ferry approaches the jetty, so the distance from the buzzer to the friend shrinks. Each crest has a shorter trip than the one before. The friend hears f > f₀.
(c) The passenger still moves with the buzzer, so she still hears f₀: no change. The friend now has the separation shrinking faster. A greater relative speed gives a greater shift, so the friend hears a frequency even further above f₀ than before.
| Point | What earns it |
|---|---|
| 1 | Rejects the claim: the passenger hears f₀ |
| 1 | Justifies with constant separation, so each crest has the same trip time and crests arrive T₀ apart |
| 1 | Notes that the steady wind does not change this (or that only relative motion matters) |
| 1 | Friend hears f > f₀ because the separation is shrinking |
| 1 | After speeding up: passenger unchanged; friend’s frequency higher still, linked to greater relative speed |
Accept an argument that the moving-source and moving-observer effects cancel because the two velocities are equal. Do not award the second point for “they are both on the ferry” with no reasoning about separation or arrival times.
How did you do?
- Q1 or Q6 wrong: re-read “A source that passes you” in the study guide. Keep pitch and loudness separate.
- Q2 or Q4 wrong: revisit “What sets the size of the shift”: direction gives the sign, relative speed gives the size.
- Q3 wrong: review “The Doppler effect for light” and the order of the spectrum.
- Q5 wrong: work through Worked example 1 again, then redo the ripple tank.
- Q7 incomplete: go back to “Why it happens: a travel-time argument”.
Then tick off the topic checklist.