Question

A 1056-hertz tuning fork is sounded at the same time a piano note is struck. You hear three beats per second. What is the frequency of the piano string?

Answer 1

Answer:

$f_2 = 1053 Hz$

or

$f_2 = 1059 Hz$

Explanation:

As we know that the beat frequency is given as

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

here we know that

$f_1 = 1056 Hz$

$f_{beat} = 3 Hz$

now we have

$|1056 - f_2| = 3$

now we have

$1056 - f_2 = \pm 3$

so we have

$f_2 = 1053 Hz$

or

$f_2 = 1059 Hz$