A violinist is tuning her instrument to concert A (440 Hz). She plays the note while listening to an electronically generated tone of exactly that frequency and hears a beat frequency of 3 Hz, which increases to 4 Hz when she tightens her violin string slightly. (a) What was the frequency of the note played by her violin when she heard the 3-Hz beats? (b) To get her violin perfectly tuned to concert A, should she tighten or loosen her string from what it was when she heard the 3-Hz beats?
"hears a beat of frequency 3.00 Hz"
So the string is 3 Hz away from 440 Hz. Add 3 Hz to 440. Subtract 3 Hz from 440. Those are the two possible values of frequency; i.e. 437 Hz and 443 Hz
"which increases to 4.00 Hz when she tightens her violin string slightly"
Tightening will raise the frequency. The possible new values are 4 Hz away from 440 Hz. Which possible value is larger than the previous possible value?
That is, given the two possible values, and the new two possible values after raising the frequency, which possibility is correct?
B. Having picked the correct value, is it more than 440 Hz or less?