AS 91523 · 2023 paper · violin tuning

Question 2(a) Achieved

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

Describe what happens to the fundamental frequency of the string when the string gets longer, with nothing else changing.

Work it out

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

1 What does a longer string do to the wavelength of its fundamental?
Makes it longer: λ = 2L.
2 With nothing else changing, what stays the same?
The wave speed on the string, because the tension and the string’s mass per unit length have not changed.
3 So what happens to the frequency?
f = v / λ: the same speed over a longer wavelength gives a lower frequency.

Answer It decreases. A longer string has a longer wavelength (λ = 2L), and with the wave speed unchanged, f = v / λ is lower.

In our words, from NZQA’s 2023 marking schedule.

How did it go?

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