NCEA 91523: wave systems (Level 3 Physics)

What NCEA 91523 assesses

NZQA's standard limits the exam to a selection of these topics: interference (quantitative) of electromagnetic and sound waves, including multi-slit interference and diffraction gratings; standing waves in strings and pipes; harmonics; resonance; beats; and the Doppler effect (stationary observer for mechanical waves). Answers can be mathematical solutions, written descriptions, graphs or diagrams. The three grades are about the depth of understanding:

• Achieved: showing awareness of how simple facets of phenomena, concepts or principles relate to a given situation.
• Merit: in-depth understanding, giving explanations for the phenomena, concepts or principles.
• Excellence: comprehensive understanding, connecting concepts or principles that relate to the situation.

The NCEA 91523 exam in 2026 and 2027

NCEA 91523 is one of three Level 3 Physics externals, with 91524 (mechanical systems) and 91526 (electrical systems). The 2026 Level 3 Physics exam is on Thursday 12 November, in the afternoon session. NZQA's 2027 timetable is not out yet: it says exams run from 9 November to 3 December 2027. The 2026 and 2027 specifications match, and say:

• Equipment: an approved calculator, a ruler and a protractor.
• Given: g = 9.81 m s⁻², and the 2025 exam came with a resource booklet (L3-PHYSR).
• Working: answers need correct units and sensible significant figures. In a "show that" question write down unrounded values.
• Maths and words: you may need to show mathematically that two phenomena or principles are connected.

How NCEA 91523 is marked: grade score marking

Each question scores N0 to E8 and the three add to 24. Counting units of a, m and e evidence, a labelled standing-wave sketch banks an easy a, while explaining why a Doppler shift occurs supplies m or e.

NCEA 91523 cut scores

These are NZQA's cut scores for the total out of 24, taken from each year's assessment schedule. Over these five years Achieved needed 7 or 8, Merit 13 or 14, and Excellence 19 or 20. The 2026 cut scores will appear in NZQA's 2026 schedule once the exam has been marked.

Worked examples at each grade

Achieved: a diffraction grating

Light of wavelength 500 nm hits a grating with 600 lines per millimetre. Find the angle of the first-order maximum. The slit spacing is d = 1 ÷ 600 000 m = 1.67 × 10⁻⁶ m, and nλ = d sin θ gives:

Merit: the Doppler effect, explained

An ambulance siren of 700 Hz approaches a stationary observer at 25 m s⁻¹. The speed of sound is 340 m s⁻¹. The observer hears:

Once it passes and moves away, the observed frequency is 700 × 340 ÷ 365 = 652 Hz. Merit gives the explanation as well as the numbers: the source moves between emitting wavefronts, so the observer meets wavefronts closer together (shorter wavelength) when it approaches, and further apart when it leaves, while the speed of sound in air stays the same.

Excellence: beats and tension

A guitar string and a 440 Hz tuning fork together give 5 beats per second. After the string is tightened a little, there are 2 beats per second. What was the string's original frequency? Beats occur at the difference between the two frequencies:

Tightening increases the wave speed on the string, v = √(T ÷ μ), so its frequency goes up. The beat frequency went down, so the string must have been below the fork and moved closer to it: it was 440 − 5 = 435 Hz, and is now 438 Hz. Excellence connects the beat equation, the effect of tension on frequency and the direction of the change, to rule out 445 Hz. Do not link beats to path difference, which NZQA's 2025 report says some candidates did.

Try the wave equation in our Light and Energy course, then press Mark to check your answer in the course:

Exam answers

The answers and a worked mark scheme come with today's paper once it is marked. We do not publish official or past paper answers. Every question on the daily paper is our own.

Use the daily paper as a practice exam

Uni-Sine publishes a free daily paper on the NCEA Level 3 Physics track. It is a short timed paper of 8 questions worth 25 to 35 marks, not a full NCEA exam, and it is not written by NZQA. Its topics are circular motion, simple harmonic motion, fields, capacitors, electromagnetic induction and nuclear physics. Waves are not among them, so for 91523 use the daily paper for general exam practice and your class notes for waves; see the NCEA Level 3 Physics guide for the whole subject.

Common mistakes in NCEA 91523

NZQA's 2025 report on the Level 3 Physics exams lists these for 91523:

• Confusing diffraction with interference.
• Linking path difference to beats. Beats come from two close frequencies.
• Everyday language. Use Level 3 ideas such as phase, not "peaks and troughs".
• Early rounding. Carry extra significant figures: the report says it caused answers up to 15% out.

Read next

New Zealand · NCEA Level 3NCEA Level 3 Physics: standards, exam date and practiceNCEA Level 3 Physics explained: wave, mechanical and electrical systems externals, the internals, the 2026 exam date, 2027 dates and worked examples.