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The label has been scratched off a tuning fork and you need to know its frequency. From its size, you suspect that it is somewhere around 250 Hz. You find a 250-Hz tuning fork and a 270-Hz tuning fork. When you strike the 250-Hz fork and the fork of unknown frequency, a beat frequency of 5 Hz is produced. When you strike the unknown with the 270-Hz fork, the beat frequency is 15 Hz. What is the unknown frequency? O 275 Hz O There is not enough information O 255 Hz O 265 Hz O 245 Hz

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Answer:

255 Hz

Explanation:

The beat frequency is the difference in frequency between two frequencies that are close.

Let the the unknown frequency be [tex]f[/tex].

Sounded with the 250 Hz tuning fork,

[tex]|250-f|=5[/tex]

[tex]f = 255 \text{ or } 245[/tex]

Sounded with the 270 Hz tuning fork,

[tex]|270-f|=15[/tex]

[tex]f = 255 \text{ or } 285[/tex]

The common value of [tex]f[/tex] in both situations is 255 Hz.

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