Beats happen when two sound waves with nearly the same frequency overlap and interfere. Instead of hearing two separate pitches, you often hear one tone that grows louder and quieter in a regular pattern. This pulsing effect is important because it makes wave interference easy to hear.
Musicians, audio engineers, and physicists use beats to compare frequencies very precisely.
The beat pattern comes from alternating constructive and destructive interference. When the two waves line up, their amplitudes add and the sound is louder. When one wave is partly out of step with the other, they cancel more and the sound is quieter.
The number of loud pulses per second is the beat frequency, given by fbeat = |f1 - f2|.
Key Facts
- Beats occur when two waves of similar frequency overlap and interfere.
- Beat frequency is fbeat = |f1 - f2|.
- Constructive interference makes the combined sound louder when wave crests align.
- Destructive interference makes the combined sound quieter when crests align with troughs.
- If f1 = 440 Hz and f2 = 444 Hz, then fbeat = 4 Hz.
- As two frequencies get closer together, the beats become slower.
Vocabulary
- Beat
- A beat is a repeating rise and fall in loudness caused by interference between two waves with slightly different frequencies.
- Frequency
- Frequency is the number of wave cycles that pass a point each second, measured in hertz.
- Interference
- Interference is the combination of overlapping waves that can increase or decrease the total amplitude.
- Constructive interference
- Constructive interference occurs when waves add together to produce a larger amplitude.
- Destructive interference
- Destructive interference occurs when waves partially or completely cancel to produce a smaller amplitude.
Common Mistakes to Avoid
- Adding the two frequencies to find the beat frequency is wrong because beats depend on the difference between the frequencies, not their sum.
- Forgetting the absolute value in fbeat = |f1 - f2| is wrong because beat frequency cannot be negative.
- Assuming beats only happen with sound is wrong because the same interference idea applies to many kinds of waves, including light and water waves.
- Thinking louder regions mean the original waves have changed frequency is wrong because the beat pattern changes amplitude while the original frequencies remain the same.
Practice Questions
- 1 Two tuning forks have frequencies of 256 Hz and 260 Hz. What beat frequency is heard?
- 2 A guitar string produces 3 beats per second when played with a 440 Hz tuning fork. What are the two possible frequencies of the guitar string?
- 3 A musician hears beats slow down while tightening a string to match a reference pitch. Explain what this means about the string frequency compared with the reference frequency.