AS 91523 · 2023 paper · violin tuning

Question 2(b) Merit

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.

Sam plays the string while sounding a tuning fork that always vibrates at 196 Hz, and hears a beat.

Describe what is meant by a beat, and explain why beats are heard.

The 2023 paper, page 4 ↗ Marking schedule, page 3 ↗

Work it out

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

1 What do you actually hear when the string and the fork sound together?
One note whose loudness rises and falls regularly: loud, soft, loud. Each loud pulse is a beat.
2 The two frequencies are close but not equal. What happens to the phase between the two waves over time?
It keeps drifting: the waves come into step, slide out of step, then come back into step, over and over.
3 What do you hear when they are in phase, and when they are 180° out of phase?
In phase they interfere constructively, and the sound is loud. 180° out of phase they interfere destructively, and the sound is quiet.

Answer A beat is a regular rise and fall in the loudness of the sound. The string and the fork have slightly different frequencies, so their waves keep drifting into and out of phase: in phase they interfere constructively (loud), 180° out of phase destructively (quiet).

What the marker wanted

Achieved Describes the change in volume, or links phase to loudness: loud when the waves are in step, quiet when they are 180° apart.
Merit Both: the change in volume, and loud when in step, quiet when 180° apart.

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

Common mistake

Explaining beats with antinodes or with a path difference. NZQA’s 2023 report lists both: beats happen at one place, over time, as two slightly different frequencies drift in and out of phase.

How did it go?

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