Piano tuners tune pianos by listening to the beats between the harmonics of two
ID: 1588909 • Letter: P
Question
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 656 Hz. What is the frequency difference between the third harmonic of the A and the second harmonic of the E? 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 includes that the E string kis properly tuned? 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?Explanation / Answer
a), b) The 2nd. harmonic of 659 Hz. is 1318Hz.
The 3rd. harmonic of 440Hz = 1320 Hz.
Beat expected = 2Hz
c) 1320 + 4 = 1324
frequency of E = 1324/2 = 662 Hz