A tuning fork that vibrates at precisely 512 Hz is sounded at the same time as a piano string. When the string is first struck, 8 loudness maxima are heard each second. The pianist then tightens the string very slightly, raising the tension so that the beat rate falls to 4 maxima per second.
(a) Determine the two possible initial frequencies of the piano string before any adjustment.
(b) Explain how the change in beat rate after tightening the string indicates whether the string’s initial frequency was higher or lower than 512 Hz.
(c) Using your reasoning from part (b), state the piano string’s initial frequency and its frequency after it is tightened.