Acoustic beats
How the Acoustic Beat Effect is Used in Electronic Music
Author:
Title 4
Learning objectives :
This experience allows students to discover the phenomenon of acoustic beats and its musical applications. It develops their auditory perception while illustrating the principles of wave interference.
Concepts covered
Wave interference, Sine wave superposition, Auditory perception, Frequency and period, Amplitude modulation
What students will do :
The student uses the FizziQ synthesizer to simultaneously produce two sounds of very close frequencies (440 Hz and 441 Hz) and observes the regular variations in sound intensity that result. Using the sound intensity sensor, it measures the period of the beat and verifies that its frequency corresponds to the difference between the two frequencies emitted. The experiment is repeated with different frequency deviations to establish the general rule.
What is required :
Smartphone with the FizziQ application, A quiet environment, Optionally headphones for better perception
Scientific background :
The phenomenon of acoustic beats results from the superposition of two sound waves of slightly different frequencies. Mathematically, when two sinusoidal waves of frequencies f₁ and f₂ add together, the resulting wave can be expressed as a single wave whose amplitude varies periodically: 2A·cos[2π(f₁-f₂)t/2]·cos[2π(f₁+f₂)t/2]. This formula shows that the resulting wave has an average carrier frequency (f₁+f₂)/2, modulated by a frequency envelope (f₁-f₂)/2. The ear thus perceives a medium frequency sound whose intensity varies at the frequency |f₁-f₂|. This phenomenon is widely used in music: for tuning instruments (the absence of beats indicates identical frequencies), and in electronic music where the LFO (Low Frequency Oscillation) effect creates rhythmic modulations. The perceptual limits are important: below 0.5 Hz, the beats are too slow to be perceived as a pulsation; beyond 20 Hz, they exceed the temporal resolution limit of the ear.