Final answer:
Beat frequencies occur when two tones of slightly different frequencies are played together. In this case, when playing the piano keys F, F-sharp, and G together, which have frequencies of 349 Hz, 370 Hz, and 392 Hz, the beat frequencies produced are 21 Hz and 22 Hz.
Step-by-step explanation:
When adjacent keys on a piano, specifically the F, F-sharp, and G notes, which have frequencies of 349 Hz, 370 Hz, and 392 Hz respectively, are played together, they create beat frequencies. Beat frequency can be calculated by finding the absolute difference between the frequencies of two sounds. In this case, the pairs of frequencies to consider are 349 Hz and 370 Hz, and then 370 Hz and 392 Hz.
The beat frequencies are the results of these calculationsThe difference between 349 Hz and 370 Hz is 21 HzThe difference between 370 Hz and 392 Hz is 22 HzTherefore, the two beat frequencies that are produced by this discordant combination of piano keys are 21 Hz and 22 Hz.The key signature from bar 87 depends on the musical composition or piece being referred to. In Western music notation, the key signature is represented by sharps (#) or flats (b) placed at the beginning of a musical staff to indicate the key of the piece. To determine the key signature at bar 87, you would need to look at the previous measures or notes to identify the key and any accidentals used. Once you know the key signature, you can determine which notes are altered throughout the piece.