Question

A piano tuner is using a 392 Hz tuning fork to tune the wire for a G-Natural note. She hears 4 beats per second. What are the two possible frequencies the piano wire is vibrating at?

Answer 1

A beat is an interference pattern between two sounds of slightly different frequencies, perceived as a periodic variation in volume whose rate is the difference of the two frequencies. Frequency beat is equal to,

$f_{beat} =| f_2\pm f_1 |$

The reference frequency in our case would be 392Hz, and since there is the possibility of the upper and lower range for the amount of beats per second that the two possible frequencies are heard would be

$f_{beat} =|392+4|= 396Hz$

$f_{beat} =|392-4|=388Hz$

Therefore the two possible frequencies the piano wire is vibrating at, would be 396Hz and 388Hz