← Wave Systems: past papers
AS 91523 · 2023 paper · Sam's violin
Question 1(a) Achieved
Practises Standing waves & resonance
A violin's strings are fixed at both ends, 0.331 m apart, and Sam makes them vibrate with a bow. One string, the "G", plays a fundamental frequency of 196 Hz. Assume the speed of sound in air is 342 m s⁻¹.
| L | 0.331 m |
|---|---|
| f₁ | 196 Hz |
| v sound | 342 m s⁻¹ |
Calculate the speed of the wave that travels along the string.
Work it out
Try it on paper first. Stuck? Take one hint at a time.
-
1 What wavelength goes with the fundamental of a string fixed at both ends?
One loop fills the string, so the string is half a wavelength: λ = 2L = 2 × 0.331 = 0.662 m. -
2 Which equation turns that into a speed?
v = fλ = 196 × 0.662 = 129.75 m s⁻¹ -
3 Is that the speed of the sound Sam hears?
No. It is the speed of the wave along the string. The sound in the air travels at 342 m s⁻¹; the string and the air share the frequency, 196 Hz, not the speed.
What the marker wanted
- Achieved The right speed, by any valid method.
In our words, from NZQA’s 2023 marking schedule.
✕Common mistake
Taking the wavelength as 0.331 m, the length of the string. NZQA’s 2023 report lists not knowing how a string’s length sets its wavelength among answers that did not reach Achieved: the fundamental is half a wavelength, so λ = 2L.How did it go?
Got it moves it further out. Review brings it back tomorrow.