While Attempting To Tune The Note C

While attempting to tune the note C at 523 Hz, a piano tuner hears 2 beats/s between a reference oscillator and the string.
(a) What are the possible frequencies of the string?
(b) When she tightens the string slightly, she hears 3 beats/s. What is the frequency of the string now?
(c) By what percentage should the piano tuner now change the tension in the string to bring it into tune?

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