Interference
36 Beats
What are beats?
If you’re a musician, you’ve probably heard the sound that results when you two sounds with almost the same pitch are played together. The result is sound with a distinctive “wah-wah-wah” sound. The pitch is about the same as the two sounds that are combining, but there is a characteristic “in and out” sound as the sound cycles back and forth between being loud and being soft. This sound is called beats. If the two notes creating the beats are really close together, the “beating” is slow- the “wahs” are long and the silences in between don’t occur very often- the beat frequency is low. If the two notes are farther apart, the beat frequency is higher- the “wahs” happen more often. Musicians use beats to tune musical instruments. (This video shows how to tune a bass guitar using beats)[1].
If you’ve never heard beats before, here are some online resources to check out:
- An interactive beats generator, [2] and/or
- Lots of info and recordings of beats. [3] Scroll to the bottom of the page to see the recordings.
- Physics classroom demo using tuning forks. [4]
What’s happening?
What causes beats?
Beats are another example of interference. As the two sounds that are being played together drift into and out of phase, the two waves shift back and forth from constructive interference to destructive interference. The silence between the “wahs” is caused by destructive interference between the two source sounds.
If the two source frequencies are nearly identical, it takes a very long time for the sounds to drift into (or out of) phase. This results in a low beat frequency. If the frequencies are farther apart, the two sounds drift in and out of phase more often, resulting in a higher beat frequency. The math is simple:
[latex]f_b = |f_1-f_2|[/latex]
In this equation, [latex]f_b[/latex] represents the beat frequency; [latex]f_1[/latex] and [latex]f_1[/latex] represent the frequency of the sounds causing the beats. If a 100 Hz sound is played with a 98 Hz sound, the result is a sound with a beat frequency of 2 Hz (according to the equation). In practical terms, there will be two full “wahs” per second. If the two sounds start in phase, they won’t be in phase again until the two source sounds drift out of phase by exactly one full cycle. Each second, the 100 Hz gains two full cycles on the 98 Hz sound, so the sounds are in phase twice every second.
At the beginning of this section on beats, it was mentioned that the listener hears a single note that fluctuates in volume (at the beat frequency). It seems logical that the frequency of this single note would be halfway between the two frequencies being played together. With a little math beyond the scope of this book you can show that your intuition is correct:
[latex]f = \frac{f_1+f_2}{2}[/latex]
So, if you play a 98 Hz note and 100 Hz note together, you hear a 99 Hz note that goes through two full cycles of “loud-soft” each second.
Stop to think
Is is possible to produce