Understanding the Underlying Physics of Beat Frequencies and Their Musical Applications
The pulsing sound you hear when two slightly out-of-tune instruments play similar notes is known as beat frequencies. This phenomenon is a result of the interaction between two sounds of slightly different frequencies. When two sounds with slightly different frequencies are played simultaneously, the air pressure waves they produce interfere with each other, leading to a pattern of alternating constructive and destructive interference. The rate of this alternation is what we perceive as a pulsing or beating sound.
The beat frequency can be calculated by taking the absolute difference between the two frequencies. For example, if one instrument plays at 440 Hz and another at 442 Hz, the beat frequency would be 2 Hz, resulting in a pulsing sound that rises and falls twice per second. This effect is commonly used in music to help musicians tune their instruments by listening for the beats and adjusting until they disappear.
The Implications of Increasing Frequency Differences
When the difference between two frequencies increases, the phenomenon takes on different names and plays a role in various phenomena, including audio interference and ring modulation.
Audio Interference and Digital Sampling
One significant example of audio interference is the principle behind why digital sampling requires a frequency more than twice the maximum frequency to be captured. This is known as the Nyquist-Shannon sampling theorem. If the highest note you want to capture is 20,000 Hz and your sampling frequency is 30,000 Hz, the difference will be 10,000 Hz, which is clearly audible as heterodyning.
As the frequency of the sound goes down, the interference frequency goes up. For instance, if you sample 20 kHz at 44 kHz, the difference is 24 kHz. With a good enough filter, you can eliminate this 24 kHz tone without affecting your 20 kHz target. This is crucial in numerous applications, including power supplies that use switching. If the frequency of the power supply is too close to some frequency you need, like sound or a digital sampler, they can interfere with each other.
Musical Effects: Ring Modulation
A musical effect called ring modulation (RM) utilizes the concept of beat frequencies in a unique way. In an RM, a carrier tone is combined with the input audio, and the output is the beat frequency, the difference between them, and the sum of the two. Most RMs filter out the carrier but output the sum and the difference, and sometimes the input waveform. As the input waveform nears the carrier frequency, the sum approaches an octave, and the difference resolves to beating, which sounds quite good. However, as the input frequency drifts away, the results don't bear any musical relationship to the input frequency, and you get these strange "clangy" noises.
This effect can become even more complex when the carrier frequency is allowed to follow the input frequency or varied with a knob. This creates a dynamic and evolving sound, often used in synthesizers and electronic music to create unique and interesting textures.
Conclusion
The phenomenon of beat frequencies and the related concepts of audio interference and ring modulation offer a rich field of study in sound engineering and music production. Understanding these principles can greatly enhance one's abilities in tuning, signal processing, and creating novel musical effects. By delving into the physics behind these phenomena, musicians and audio engineers can unlock a wealth of creative possibilities in their work.