Final answer:
F Sharp and G Flat are the same pitch, known as enharmonic equivalents. When F (349 Hz), F# (370 Hz), and G (392 Hz) are struck on a piano, two sets of beat frequencies are produced: 21 Hz between F and F#, and 22 Hz between F# and G.
Step-by-step explanation:
The note represented by F Sharp (F#) and G Flat (G♭) on the staff is, in fact, the same pitch in Western music, a concept known as enharmonicism. In a system known as equal temperament, which is used on modern pianos, these two notes are enharmonic equivalents. However, when it comes to beat frequencies, we are dealing with a phenomenon that occurs when two tones with slightly different frequencies are played simultaneously.
When three adjacent keys on a piano such as F, F-sharp, and G are struck together, resulting in frequencies of 349 Hz, 370 Hz, and 392 Hz respectively, two sets of beat frequencies will be produced. The first set of beats will occur between the F and F-sharp notes, with a frequency of 370 Hz minus 349 Hz, which equals 21 Hz. The second set of beats will occur between the F-sharp and G notes, with a frequency of 392 Hz minus 370 Hz, which also equals 22 Hz.