Question

Three adjacent keys on a piano (F, F-sharp, and G) are struck simultaneously, producing frequencies of 349, 370, and 392 Hz. What beat frequencies are produced by this discordant combination?

a) 21 Hz and 22 Hz
b) 1 Hz and 2 Hz
c) 18 Hz and 22 Hz
d) 2 Hz and 3 Hz

Answer 1

The discordant combination of piano keys F, F-sharp, and G struck simultaneously at frequencies of 349 Hz, 370 Hz, and 392 Hz, respectively, produces beat frequencies of 21 Hz and 22 Hz.

Step-by-step explanation:

When three adjacent keys on a piano (F, F-sharp, and G) are struck simultaneously, producing frequencies of 349 Hz, 370 Hz, and 392 Hz, beat frequencies are generated due to the interference of these sound waves. The beat frequencies can be found by calculating the absolute differences between the pairings of the frequencies.

• For F (349 Hz) and F-sharp (370 Hz), the beat frequency is |349 Hz - 370 Hz| = 21 Hz.
• For F-sharp (370 Hz) and G (392 Hz), the beat frequency is |370 Hz - 392 Hz| = 22 Hz.

Therefore, the beat frequencies produced by this discordant combination are 21 Hz and 22 Hz, corresponding to answer choice (a).