Final answer:
Beat frequencies occur when two tones with different frequencies are played simultaneously. Playing A (220 Hz) and C (264 Hz) together results in a 44 Hz beat frequency, while D (297 Hz) and F (352 Hz) create a 55 Hz beat frequency. Playing all four notes together will result in multiple beat frequencies corresponding to the differences between each pair of notes.
Step-by-step explanation:
When two musical notes with different frequencies are played together, the resulting beat frequency is the absolute difference between the two frequencies. The beat frequency is a result of the interference of sound waves, which can be constructive or destructive, leading to periodic increases and decreases in loudness heard as beats.
Beat Frequencies from Musical Notes:
- Playing A and C together: The frequencies of musical notes A (220 Hz) and C (264 Hz) will produce a beat frequency of 44 Hz, which is the absolute difference between the two frequencies (264 Hz - 220 Hz).
- Playing D and F together: The frequencies of musical notes D (297 Hz) and F (352 Hz) will result in a beat frequency of 55 Hz, which is the absolute difference (352 Hz - 297 Hz).
- Playing A, C, D, and F together: If all four notes are played together, multiple beat frequencies could be present. The beats would be found by taking the absolute differences between all combinations of the four frequencies:
- A (220 Hz) and C (264 Hz): 44 Hz
- A (220 Hz) and D (297 Hz): 77 Hz
- A (220 Hz) and F (352 Hz): 132 Hz
- C (264 Hz) and D (297 Hz): 33 Hz
- C (264 Hz) and F (352 Hz): 88 Hz
- D (297 Hz) and F (352 Hz): 55 Hz
The ear perceives these beat frequencies as variations in the loudness of the sound, occurring at the beat frequency rate.