Question 3(d) Merit to Excellence

Jane and her classmates stand on a railway platform, listening to a train approach them at a constant speed, blowing its whistle. The speed of sound in air is 343 m s⁻¹.

Another train approaches and goes past them without stopping. A graph on the paper shows the frequency they hear against the train's position, marked Section A (approaching), Point B (right in front of them) and Section C (going away), with a line at the whistle's actual frequency.

Using the shape of the graph, explain what may be happening (i) as the train approaches (Section A), (ii) as it is right in front of them (Point B), and (iii) as it goes away (Section C).

You need the paper’s diagram for this part. It is a graph of the frequency Jane and her friends hear against the train’s position, with Section A, Point B and Section C marked and a line at the whistle’s actual frequency. The 2024 paper, page 8 ↗

Marking schedule, page 6 ↗

Work it out

Try it on paper first. Stuck? Take one hint at a time.

1. 1 Read the graph. Where is the frequency above the actual frequency, and where below? Which way is it heading in each section?

   In Section A it is above the actual frequency and rising as the train gets nearer, until just before B. It drops steeply through the actual frequency at Point B. In Section C it is below the actual frequency and still falling as the train moves away.

2. 2 Section A: what would make the shift keep growing while the train approaches?

   Above the actual frequency means the train is approaching. The shift grows with the speed towards the listener, f′ = f × v / (v − v_s), so a frequency that keeps rising means v_s is growing: the train is speeding up as it comes. (At a steady speed it would fall slowly instead, as the line to them swings round, so a rise can only mean speeding up.)

3. 3 Point B: how much of the train’s velocity is towards or away from them at that moment?

   None. Right in front of them, the train is moving neither towards them nor away, so there is no Doppler shift: they hear the whistle’s actual frequency, where the curve crosses that line.

4. 4 Why is the drop so steep around B?

   They are on the platform, beside the track rather than on it, so the train passes a little to one side of them. Close to B the line from the train to them swings round quickly: the part of the velocity towards them falls to zero, and the part away from them builds up, within a short distance. That swing happens at any speed.

5. 5 Section C: what does a frequency below the actual one, and still falling, tell you?

   Below means the train is moving away. Just after B the frequency would fall even at a steady speed, while the line to them is still swinging round. But it is still falling right across Section C, long after B, where that swing has finished. So the shift is still growing, f′ = f × v / (v + v_s), and v_s is still increasing: the train keeps speeding up as it leaves.

What the marker wanted

• Achieved Identifies two of: a higher pitch that is rising (A); the actual frequency when the train is in front of them (B); a lower pitch that is falling (C).
• Merit Explains one of those three.
• Excellence Explains all three.

In our words, from NZQA’s 2024 marking schedule.

Common mistake

How did it go?

Got it moves it further out. Review brings it back tomorrow.