Question

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? Select the correct answer O 275 Hz O There is not enough information O 255 Hz O 265 Hz O 245 Hz

Answer 1

The difference in frequency is given as:

$f=\left | f_{1}-f_{2} \right |$

Let the unknown frequency be f.

Thus, when hit with a 250 Hz folk,

5 = 250-f f = 245 Hz

or

5 = f-250 and f = 255 Hz

When hit with a 270 Hz folk,

15 = 270-f and f = 255 Hz

or 15 = f- 270 and f = 285 Hz

The common frequency in both the cases is 255 Hz.

Thus, the answer is 255 Hz