(Solution) - To tune a violin the violinist first tunes the A -(2025 Original AI-Free Solution)

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To tune a violin, the violinist first tunes the A string to the correct pitch of 440 Hz and then bows two adjoining strings simultaneously and listens for a beat pattern. While bowing the A and E strings, the violinist hears a beat frequency of 3 Hz and notes that the beat frequency increases as the tension on the E string is increased. (The E string is to be tuned to 660 Hz.)
(a) Why is a beat produced by these two strings bowed simultaneously?
(b) What is the frequency of the E string vibration when the beat frequency is 3 Hz?
(c) If the tension on the E string is 80.0 N when the beat frequency is 3 Hz, what tension corresponds to perfect tuning of that string?