Question

A 3580 Hz tuning fork is sounded at the same time that a note on a piano is struck. You hear 8 beats/s. You loosen the string slightly and now hear 12 beats/s. What is the frequency of the vibrating piano string now after the loosen ing?

Answer 1

you hear the difference frequency
8 = 3580 - f
f = 3472 original

12 = 3580 -f
f = 3568 final
good, the frequency went down when I loosened the string

so 3568 Hz

WHAT if I wrote the difference the other way (all I know is the absolute value)
8 = f - 3580
f = 3588
12 = f - 3580
f = 3592
oh my the frequency went up when we loosened the string - no way so the difference is the other way around
and
3568 is the answer