Final answer:
Beat frequencies are produced by the interference of sound waves with different frequencies. For the piano keys F (349 Hz), F-sharp (370 Hz), and G (392 Hz), the beat frequencies produced are 21 Hz between F and F-sharp, and 22 Hz between F-sharp and G.
Step-by-step explanation:
When three adjacent keys on a piano are struck simultaneously, each producing different frequencies, beat frequencies are produced as a result of the interference patterns between the different sound waves. In this case, the keys struck are F, F-sharp, and G, which correspond to frequencies of 349 Hz, 370 Hz, and 392 Hz, respectively.
Beat frequency is calculated as the absolute difference between the frequencies of two tones. For F and F-sharp, the beat frequency will be the absolute difference between 349 Hz and 370 Hz, which is 21 Hz. For F-sharp and G, the beat frequency will be the absolute difference between 370 Hz and 392 Hz, which is 22 Hz. These beat frequencies are audible and can be perceived as a wobbling or pulsing sound when the notes are played together.