What are beats? Explain how they are produced, and show that the beat frequency equals the difference in the frequencies of the two sources.
How to lay out the answer. Follow the frame, then write it in your own words.
1 · Define beats. The regular rise and fall of loudness when two sounds of slightly different frequencies are heard together.
2 · Set up the two sources. Forks A and B have frequencies N and N + n, with n small (less than about 10).
3 · Follow the phase.
t = 0: both in phase, so the sound is loud
t = 1/(2n) s: B has gained half a vibration, so they are opposite in phase and the sound is faint
t = 1/n s: B has gained one vibration, so they are in phase and the sound is loud again
4 · Draw the graph. [Two displacement-time graphs of slightly different frequencies, and their sum with swelling and shrinking height; one beat period 1/n marked]
5 · Conclude. One beat every 1/n s gives n beats per second, and n = (N + n) − N.
6 · Real life. Musicians tune an instrument by adjusting it until the beats with a reference note disappear.
Scoring tip: Show the three moments (in phase, opposite phase, in phase again) clearly; they are the heart of the answer.
