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# Problem: 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?

###### FREE Expert Solution

Let's consider two sounds in this problem.

In the case where you're listening to two sounds that have different frequencies, you'll hear distant tones.

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###### Problem Details

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?