AS 91523 · 2025 paper · Doppler effect

Question 1(b) Merit

Martyn and Kerryn are riding jet skis on a lake. Martyn's jet ski has an air horn that emits 1043 Hz. Kerryn stops, and Martyn travels directly towards her at 27.3 m s⁻¹. The speed of sound in air is 343 m s⁻¹.

f source	1043 Hz
v source	27.3 m s⁻¹
v sound (air)	343 m s⁻¹

Explain why Kerryn hears a different frequency from the one the air horn emits.

The 2025 paper, page 2 ↗ Marking schedule, page 1 ↗

See it move: The Doppler effect: a moving source and a moving observer

Work it out

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

1 Each wavefront spreads out from wherever the horn was when it sent it. Where is the horn when it sends the next one?
A little closer to Kerryn. In one period it moves v_sT = 27.3 / 1043 ≈ 0.026 m towards her, so every wavefront starts slightly nearer to her than the one before.
2 What does that do to the spacing of the wavefronts on Kerryn’s side?
They are closer together: the wavelength ahead of the jet ski is shorter than a horn at rest would give. (Behind it they are spread further apart.)
3 Does the sound travel any faster because the horn is moving?
No. The speed of sound is set by the air, so it stays 343 m s⁻¹ whatever the horn does.
4 Put those two together with v = fλ. What must happen to the frequency she hears?
The same speed with a shorter wavelength means more wavefronts reach her every second: f = v / λ is higher. That is the 1133 Hz from (a).

Answer The horn moves towards Kerryn, so each wavefront is sent out a little closer to her than the last and the wavelength reaching her is shorter. The speed of sound in air does not change, so by v = fλ the frequency she hears is higher.

What the marker wanted

Achieved One of the three ideas: she hears a higher frequency; the wavelength is shorter; or the speed of sound stays the same.
Merit All three together: the shorter wavelength, the unchanged speed of sound, and so the higher frequency.

In our words, from NZQA’s 2025 marking schedule.

Common mistake

Saying the waves “bunch up” and stopping there, or saying the sound gets louder. NZQA’s 2025 report lists both among answers that did not reach Achieved. Say what the bunching does to the wavelength, and talk about frequency, not volume.

How did it go?

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