Wave Systems

Practice

Recall it first, then use it — testing yourself builds the memory, where rereading the notes above only feels easier.

Recall and application shuffled together — you have to work out what each item wants before you can answer it, which is the part the exam actually tests. Both kinds feed the same spacing schedule, so anything you miss comes back sooner.

Say the answer out loud before flipping — that attempt is where the learning happens, even when you get it wrong.

Exam-style only. Instant feedback, shuffled each attempt, best score saved on this device.

What actually comes up

Three years of real questions, part by part, with the grade band each part sat at according to that year's marking schedule. Start with the pattern table — it is the fastest way to decide what to revise.

Across 3 years

The pattern — what to prepare

The 2025 paper ↗ Marking schedule ↗

Question 1 — Doppler effect

Martyn and Kerryn are riding jet skis on a lake. Martyn's jet ski has an air horn emitting 1043 Hz. Kerryn stops, and Martyn travels directly towards her at 27.3 m s⁻¹.

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

• a Calculate the frequency of the sound that Kerryn hears. Achieved
• b Explain why Kerryn hears a different frequency to the one emitted. Merit
• c Kerryn floats very close to the jet ski's path; her friend Erin watches from the bank. A graph shows the frequency each hears as the jet ski travels from A to C. Explain why the frequency Kerryn hears is the same as, or different to, the frequency Erin hears. Excellence
• d An underwater microphone monitors engine noise. The engine sounds at 574.0 Hz; as the jet ski travels AWAY from the microphone at 27.3 m s⁻¹ the microphone measures 563.6 Hz. Calculate the velocity of sound in water. Merit

Question 2 — standing waves

A cello's strings are supported at each end by the bridge and the nut, 0.690 m apart, and can vibrate in different harmonics.

• L = 0.690 m

• a Draw the 4th harmonic of a cello string; label nodes and antinodes. Achieved
• b After storage the string tension has decreased and the instrument is out of tune. Use v = √(tension ÷ mass per unit length). No calculations required. Explain how this could make the frequency higher or lower than the desired one. Merit
• c The 0.690 m string's first harmonic is 147 Hz. A finger shortens the string so its first harmonic becomes 207 Hz. Tension is unchanged. Calculate the new length of the string. Merit
• d i Explain why beats form when two strings are at nearly the same frequency. Merit
• d ii Explain what you hear as the string length keeps being reduced. Excellence

Question 3 — interference patterns

A laser shines green light onto a double slit of separation 1.25 × 10⁻⁴ m. Each slit acts as an in-phase source, producing closely-spaced fringes on a screen 3.40 m away. The distance from the central maxima to the 3rd order maxima is 4.20 × 10⁻² m.

• d = 1.25×10⁻⁴ m
• L = 3.40 m
• y₃ = 4.20×10⁻² m

• a Show the green laser has λ = 515 nm (double-slit, d = 1.25×10⁻⁴ m). Achieved
• b Explain why the intensity varies across the screen. Merit
• c Swapping to a closely-spaced grating — explain every change to the pattern. Excellence
• d A green 515 nm laser is shone through a DIFFERENT diffraction grating and 7 maxima are seen. The screen is 0.900 m wide and 1.20 m from the grating. Calculate the possible range of values for the slit separation. Excellence

The 2024 paper ↗ Marking schedule ↗

Question 1 — the pan flute

A pan flute is a set of pipes of different lengths bound together, each CLOSED at one end and open at the other. Jane's shortest pipe is 8.50 cm and her longest is 17.5 cm.

• v sound = 343 m s⁻¹
• shortest pipe = 8.50 cm
• longest pipe = 17.5 cm

• a Draw the third harmonic of a pipe closed at one end; label N and A. Achieved
• b Calculate the frequency of the third harmonic in the 8.50 cm shortest pipe. Merit
• c Explain how standing waves form and why closed pipes cannot make every harmonic. Excellence
• d A cork inside the pipe adjusts its length. The untuned longest pipe produces a beat of 9.00 Hz against a tuned pipe of length 0.164 m, which plays 523 Hz on its first harmonic. Calculate how much further the cork must be pushed in, and explain how you can hear when it is in the right position. Merit

Question 2 — interference

A red laser is shone through a diffraction grating placed at the centre of a semicircular screen, giving a number of narrow bright fringes. The grating formula is nλ = d sinθ.

• 200 lines per mm
• λ = 638 nm

• a State what the term nλ represents in the grating formula nλ = d sinθ. Achieved
• b 200 lines/mm grating, 638 nm — calculate the total number of dots on the screen. Merit
• c Same laser through two slits further apart — describe and explain every difference. Excellence
• d White light on the grating — explain why violet sits on the inside of each spectrum. Merit

Question 3 — Doppler effect

Jane and her classmates stand on a railway platform as a train approaches at constant speed, blowing its whistle.

• v sound = 343 m s⁻¹

• a State what Jane and her friends hear compared to the train driver (pitch). Achieved
• b Explain why a change in frequency is heard as the train approaches. Merit
• c They hear 1270 Hz as the train approaches, and 1190 Hz after it has passed, receding at the same constant speed. Calculate the speed of the train. Merit
• d A frequency-vs-position graph is given for a train that passes without stopping, marked Section A (approaching), Point B (right in front of them) and Section C (receding). Explain what is happening in Section A and at Point B, in terms of frequency and position. Excellence

The 2023 paper ↗ Marking schedule ↗

Question 1 — Sam's violin

A violin's strings are fixed at both ends, 0.331 m apart. Sam plays the "G" string, which has a fundamental frequency of 196 Hz.

• L = 0.331 m
• f₁ = 196 Hz
• v sound = 342 m s⁻¹

• a Calculate the speed of the wave that travels along the string. Achieved
• b The sound produced also contains vibrations at 392 Hz and 588 Hz. State the harmonic causing the vibration at 588 Hz, and sketch its nodes and antinodes. Merit
• c Sam plays the violin sitting on a trailer moving at 5.30 m s⁻¹ directly towards microphone A. Calculate the frequency recorded by microphone A. Merit
• d Microphone B is directly behind the moving trailer; microphone A is directly in front. Explain how the trailer's motion affects the frequency of the string, the speed of sound in air, the wavelength in front of and behind the violin, and the frequencies at A and B. Excellence

Question 2 — violin tuning

On a hot day the violin goes out of tune, and Sam has to adjust the tension in the string to keep the "G" vibrating at 196 Hz.

• a Explain why increasing string length lowers the frequency produced. Achieved
• b Explain what beats are and why they are heard (in phase / out of phase). Merit
• c Tuning a string toward 196 Hz with beats — decide whether it is at 198.1 or 193.9 Hz, and justify. Excellence
• d i Name resonance and explain why shifting the violin makes the wine glass rattle. Excellence
• d ii Suggest a way to stop the wine glass from rattling. Merit

Question 3 — diffraction glasses

At a fair, children buy “Rainbow Glasses” made of diffraction gratings in a cardboard frame. Steve shines a laser pointer through one of the gratings onto a wall. The laser produces light of wavelength 643 nm (6.43 × 10⁻⁷ m). The pattern on the wall has a bright red spot at the centre and slightly dimmer red spots either side. The wall is 1.43 m from the grating, and the distance from the central bright spot to the second slightly dimmer spot is 1.75 m.

• λ = 643 nm (6.43 × 10⁻⁷ m)
• grating to wall 1.43 m
• centre to 2nd order 1.75 m

• a Describe diffraction. Achieved
• b Give an in-depth explanation why this pattern is observed, by explaining how diffraction and interference cause bright spots, and explaining why there are large sections with no light between the bright spots. Excellence
• c Calculate the slit separation in the grating. Merit
• d When the children look at a spot of white light through the glasses, they see the white spot with spectra on either side (“rainbows”). Give an in-depth explanation of this phenomenon by describing where the spectra will occur, explaining the position of the colours in the spectra, and explaining why they are in these locations. Include a labelled sketch. Excellence

Read the last column as a to-do list. Doppler and interference appear in every paper; the Excellence rows are where a Merit becomes an Excellence.

Past exams & resources

⏱ Timed opens the paper and starts a countdown matching the exam length. Official NZQA PDFs. If a link 404s, that year’s paper may sit under a slightly different code: browse the NZQA subject page.