Final answer:
Beat frequencies occur when two musical notes with different pitches are sounded together, calculated as the absolute difference between their frequencies. When A and C (220 Hz and 264 Hz) are played together, the beat frequency is 44 Hz; for D and F (297 Hz and 352 Hz), it is 55 Hz. With all four notes, multiple beat frequencies emerge, creating complex interference patterns.
Step-by-step explanation:
When two pitches, or musical notes, are sounded together, several phenomena can occur. One of these is the creation of beat frequencies, which is the result of the interference patterns created by the two sound waves of differing frequencies. The beat frequency can be calculated as the absolute difference between the two frequencies. In the case of the musical notes A and C played together with frequencies of 220 Hz and 264 Hz, respectively, the beat frequency would be |220 Hz - 264 Hz|, which equals 44 Hz. Similarly, if D and F are played together with frequencies of 297 Hz and 352 Hz, the beat frequency would be |297 Hz - 352 Hz|, or 55 Hz. If all four notes are played simultaneously, a more complex pattern of beats will emerge, involving beat frequencies of 44 Hz, 55 Hz, and the differences between the other pairs of frequencies.
The subject of beat frequencies touches on the physics concept of superposition, where two waves combine to form a resultant wave. When dealing with harmonics and overtones in musical contexts, the superposition can create resonance, enriching the sound. Moreover, the difference in frequency between two waves, which determines the beat frequency, adds a unique texture to the music, sometimes pleasant in the form of consonance, but also potentially jarring when it results in dissonance.