Question

Two piano strings produce beats. Frequencies of the strings are 1560 Hz. and 1563 Hz. Choose the correct frequency of the beats.

Answer 1

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.

Answer 2

Beat frequency is given by the difference of two frequencies played together

$f_{beat} = |f_1 - f_2|$

given that

$f_1 = 1560 Hz$

$f_2 = 1563 Hz$

Now

$f_{beat} = |1560- 1563| Hz$

$f_{beat} = 3 Hz$