Well first of all, I have to point out that the correct frequency of the beats is not on the list of choices that you provided.
When sources with different frequencies combine, two beats are created. The beat frequencies are the sum and difference of the frequencies that produce them.
If the source frequencies are 1,560 Hz and 1,563 Hz, then the beat frequencies are
3 Hz and 3,123 Hz.
The 3 Hz is perceived as a slight 'vibrato' in the piano's tone, so that it sounds warmer and not like a flat sine-wave generator.
The 3,123 Hz doesn't propagate well through the structure of the piano, and isn't noticeable to anyone except an expert listener (like a piano tuner). Only the top 6 keys [out of 88] on a standard piano keyboard have frequencies of 3,123 Hz or higher.
