Beats: Two Close Frequencies Interfering
1 · Predict
Two speakers play tones that are almost the same frequency. A listener hears the loudness pulse up and down. What determines how fast it pulses?
- The pulse (beat) rate equals the difference between the two frequencies.
- The pulse rate equals the sum of the two frequencies.
- The pulse rate equals the average of the two frequencies.
2 · Set Up
- Open the two-source-beats preset and press Reset. Source 1 is fixed at 440 Hz.
- Enable the beat-frequency and carrier-frequency readouts at the observer.
- Set Source 2's frequency for each trial and record the beat frequency.
3 · Collect Data
| Source 1 frequency f₁ (Hz) | Source 2 frequency f₂ (Hz) | Carrier frequency f_c (Hz) | Beat frequency f_beat (Hz) |
|---|---|---|---|
| 440 | 442 | ||
| 440 | 444 | ||
| 440 | 448 |
Plot beat frequency f_beat (y-axis) against |f₂ − f₁| (x-axis) for your three trials.
4 · Analyze
- For one trial, compute f_beat = |f₂ − f₁| and f_c = (f₁ + f₂)/2. Compare both to the table.
- Explain why a listener perceives one tone near the carrier frequency, with loudness pulsing at the (much slower) beat frequency.
5 · Extend
- Musicians tune instruments by listening for beats between their note and a reference tone, adjusting until the beats slow to zero. Explain why zero beats means the two frequencies are exactly equal.
- As f₂ gets closer and closer to f₁, what happens to the beat frequency? What would you hear in the limit f₂ = f₁?
The Physics Behind This Experiment
Beat Frequency
When two tones of nearly equal frequency overlap, their interference pattern pulses in loudness at a rate equal to the difference between the two frequencies.
Carrier Frequency
The pitch a listener actually perceives is close to the average of the two source frequencies — the beat is a slow amplitude pulsation riding on top of that average tone.