1. Beats
AP Physics 1

2. Beats
When two notes are played that have frequencies that are close to one another, the constructive and destructive interference pattern creates “beats” in the sound.
Beats are the periodic and repeating fluctuations heard in the intensity of a sound when two sound waves of very similar frequencies interfere with one another.

3. Beat Pattern (in green)

4. Details about beats…
A beat pattern is characterized by a wave whose amplitude is changing at a regular rate.
On the previous slide, the beat pattern (drawn in green) repeatedly oscillates from zero amplitude to a large amplitude, back to zero amplitude throughout the pattern
When constructive interference occurs between two crests or two troughs, a loud sound is heard. This corresponds to a peak on the beat pattern (drawn in green). When destructive interference between a crest and a trough occurs, no sound is heard; this corresponds to a point of no displacement on the beat pattern.
Since there is a clear relationship between the amplitude and the loudness, this beat pattern would be consistent with a wave that varies in volume at a regular rate.

5. Beat Frequency
The beat frequency refers to the rate at which the volume is heard to be oscillating from high to low volume.
For example, if two complete cycles of high and low volumes are heard every second, the beat frequency is 2 Hz. The beat frequency is always equal to the difference in frequency of the two notes that interfere to produce the beats. So if two sound waves with frequencies of 256 Hz and 254 Hz are played simultaneously, a beat frequency of 2 Hz will be detected.

6. Math model for beats fbeat = f1- f2 *the aboslute value of f1-f2
For example, if we have a source producing 440 Hz frequency sound waves and a second source producing 441 Hz sound waves, then we will hear a sound with 1 “beat” per second.

7. Applications
A piano tuner frequently utilizes the phenomenon of beats to tune a piano string. She will pluck the string and tap a tuning fork at the same time. If the two sound sources - the piano string and the tuning fork - produce detectable beats then their frequencies are not identical. She will then adjust the tension of the piano string and repeat the process until the beats can no longer be heard. As the piano string becomes more in tune with the tuning fork, the beat frequency will be reduced and approach 0 Hz. When beats are no longer heard, the piano string is tuned to the tuning fork; that is, they play the same frequency. The process allows a piano tuner to match the strings' frequency to the frequency of a standardized set of tuning forks.