Problem 21.70 Piano tuners tune pianos by listening to the beats between the har

Question

Problem 21.70 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. Part 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 indicates that the E string is properly tuned? Express your answer with the appropriate units. Part 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? Express your answer with the appropriate units.

Explanation / Answer

A. 3rd harmonic of A = 440 x 3 = 1320Hz ....2nd harmonic of E = 659 x 2 = 1318Hz (Target frequency) Beat frequency = 1320 - 1318 = 2Hz (when properly tuned) B. When beat frequency is 4Hz frequency of E string = 1320 - 4 = 1316Hz.

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