AS 91523 · 2024 paper · the pan flute
Question 1(b) Merit
Practises Standing waves & resonance
A pan flute is a set of pipes of different lengths bound together, each CLOSED at one end and open at the other. Sound is made by blowing across the open ends. Jane's shortest pipe is 8.50 cm long and her longest is 17.5 cm. The speed of sound in air is 343 m s⁻¹.
| v sound | 343 m s⁻¹ |
|---|---|
| shortest pipe | 8.50 cm |
| longest pipe | 17.5 cm |
Calculate the frequency of the third harmonic produced in the shortest pipe.
Work it out
Try it on paper first. Stuck? Take one hint at a time.
-
1 How much of a wavelength fits in the pipe for the third harmonic?
Three quarters, as in (a): L = 3λ/4. -
2 Find the wavelength. Watch the units of the length.
L = 8.50 cm = 0.0850 m, so λ = 4L / 3 = 4 × 0.0850 / 3 = 0.113 33… m. Keep it unrounded in your calculator. -
3 Now the frequency.
f = v / λ = 343 / 0.113 33… = 3026.47 Hz. Rounding λ to 0.1133 m first would give 3027 Hz, so keep it unrounded. (Both round to 3030 Hz.) -
4 Check it with the closed-pipe formula.
fn = nv / 4L with n = 3: 3 × 343 / (4 × 0.0850) = 3026 Hz. The pipe’s fundamental is 1009 Hz, and the third harmonic is three times that.
What the marker wanted
- Achieved The right wavelength, 0.1133 m, or the calculation with one error.
- Merit The right frequency, about 3030 Hz.
In our words, from NZQA’s 2024 marking schedule.
✕Common mistake
Leaving the length as 8.50 instead of 0.0850 m. NZQA’s 2024 report says the handling of SI prefixes was very poor that year: convert centimetres to metres before using v = fλ.How did it go?
Got it moves it further out. Review brings it back tomorrow.