Beats
Key ideas
- Beats happen when two waves of nearly equal frequency superpose. The waves drift in and out of step, so the sound swells and fades — a slow, regular throb in loudness.
- When the two waves are in phase, they add to a loud moment (constructive).
- Half a beat later they are out of phase and cancel to a quiet moment (destructive).
- The beat frequency is the difference of the two frequencies:
- Each variable, with sub-bullets:
- — the two source frequencies (Hz)
- — the number of loud–quiet cycles heard per second (Hz)
- The closer the two frequencies, the slower the beats. Identical frequencies give no beats at all — which is exactly how instruments are tuned.
A tuning fork sounds at Hz. A guitar string played with it produces beats at Hz. What are the possible string frequencies, and how would tightening the string decide between them?
Step 1 — Apply the beat relationship
Step 2 — Two possibilities
Step 3 — Use the trend to decide
Tightening the string raises its frequency. If the beats slow down, the string was at Hz (moving toward ). If the beats speed up, it was at Hz (moving away).
Tips
- If you hear (or are told) beats over several seconds, divide by the time to get the beat frequency first — quoting the count as a frequency is a common slip.
- Keep beats and interference fringes separate in your head: beats are superposition in time (loud–quiet), fringes are superposition in space (bright–dark).
Test yourself
Practice by grade
One question each at Achieved, Merit and Excellence. Have a go, then compare with the model answer.
Two flutes play notes of Hz and Hz.
Show that the beat frequency is Hz.
A violinist hears beats in s when playing with a Hz tuning fork.
Calculate the possible frequencies of the violin string.
Explain, using superposition, why two sources of nearly equal frequency produce a sound that rises and falls in loudness, and why the effect disappears as the frequencies are made equal.