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 :

Answer:

[tex]f_2 = 1053 Hz[/tex]

or

[tex]f_2 = 1059 Hz[/tex]

Explanation:

As we know that the beat frequency is given as

[tex]|f_1 - f_2| = f_{beat}[/tex]

here we know that

[tex]f_1 = 1056 Hz[/tex]

[tex]f_{beat} = 3 Hz[/tex]

now we have

[tex]|1056 - f_2| = 3[/tex]

now we have

[tex]1056 - f_2 = \pm 3[/tex]

so we have

[tex]f_2 = 1053 Hz[/tex]

or

[tex]f_2 = 1059 Hz[/tex]

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