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In: Physics

Piano tuners tune pianos by listening to the beats between the harmonics of two different strings....

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?

Solutions

Expert Solution

A

fbeat=3fA?2fE=2Hz

B. 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)

C. When beat frequency is 4Hz
frequency of E string = 1320 - 4 = 1316Hz.

genius_generous answered 2 years ago
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