Question

78) To tune middle C on a piano, a tuner hits the key and at the same time sounds a 261-Hz tuning fork. If the tuner hears 3 beats per second, what are the possible frequencies of the piano key?

Answer 1

Take into account that the beat frequency of the sound produced by the two waves from the piano and the tuning fork, is given by:

`f_b=\lvert f_1-f_2\rvert`

where f1 and f2, in this case, are the frequencies of the piano and the tuning fork.

If f2 = 261 Hz and fb = 3, then, you can conclude that f1 (the frequency of the tune middle C on the piano) can be 263Hz, or 258Hz.

In both cases, if you use the equation above, you obtain a beat frequency equal to 3.