Physics, 22.09.2019 07:30 andrewcamp99

Piano tuners tune pianos by listening to the beats between the harmonics of two different strings. when properly tuned, the note a should have a frequency of 440 hz and the note e should be at 659 hz.
(a) what is the frequency difference between the third harmonic of the a and the second harmonic of the e?
(b) a tuner first tunes the a string very precisely by matching it to a 440 hz tuning fork. she then strikes the a and e strings simultaneously and listens for beats between the harmonics. what beat frequency between higher harmonics indicates that the e string is properly tuned?
(c) the tuner starts with the tension in the e string a little low, then tightens it. what is the frequency of the e string when she hears four beats per second?

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