In: Physics
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?
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.