thesis : beatings : theory

interference

We already listened to one tone produced from one speaker which produces a standing wave in space.
If you place two speakers in space their sound will interfere with each other.
Depending on the position of the two speakers, what they play and the phase of the sound wave, the interference pattern will be different.

When both speakers play the same sine wave (same pitch and amplitude) their energies are either added together (constructive interference) or canceled out (destructive interference) depending on their phase.

constructive interference: same phase, same frequency, same amplitude: 2 sound waves added together = loud

between constructive and destructive interference: different phase, same frequency, same amplitude

destructive interference: opposite phase, same frequency, same amplitude: 2 sound waves cancelling each other = silence

beatings

Beatings is one kind of interference pattern that happens when two tones with the same amplitude but with slightly different pitch sound together. Because one of the tones is slightly higher than the other, the wavelength will be different. This makes the interference pattern change continuously from constructive to deconstructive. We experience this as a constant alternation between sound and silence.

The frequency difference of the two tones is equal to the number of beats per second.¹⁵

Wave 1 has a higher frequency, therefor bigger amplitude than Wave 2

15. Hermann Helmholtz “On the sensations of tone”, 164 Origin of beats.
16. All animations made by Know Art Studios.

beats (music) vs beats (sound phenomenon)

1 – Beats in music are regular repeating short tones, a pulse. Normally measured in beats per second and slower than 1.200 bpm = 20 bps = 20Herz. In my thesis I will call this meaning of beats a pulse
2 – Beats as sound phenomenon is the interference pattern produced by two tones of almost the same pitch. In my thesis when I write about beats I’m referring to this sound phenomenon

Beatings are something different than a pulse.
Beatings are born from two tones.
A pulse is created from one tone sounding, not sounding, sounding, not sounding.
We do experience beatings as a pulse.
But: is the sum of the two sound waves creating beatings the same physical wave in the air as the waves of a pulse?

beatings : experiment