The A-string on a guitar has length L = 0.648 m and lin- ear mass density \mu = 4.25 g/m. If the string is perfectly in tune, then the third harmonic should have a frequency of f = 330 Hz. However, on a particular out-of-tune guitar, the A-string’s third harmonic is measured to be f ′ = 323 Hz. How much tension T must be added to the A-string in order to bring it back into tune? For the limits check, investigate what happens to T as the string gets very long. (For this problem you may ignore any slight changes to \mu that might result from the tuning process.) Please provide units and equations used.

The A-string on a guitar has length L = 0.648 m and lin- ear mass density \mu = 4.25 g/m. If the string is perfectly in tune, then the third harmonic should have a frequency of f = 330 Hz. However, on a particular out-of-tune guitar, the A-string’s third harmonic is measured to be f ′ = 323 Hz. How much tension T must be added to the A-string in order to bring it back into tune? For the limits check, investigate what happens to T as the string gets very long. (For this problem you may ignore any slight changes to \mu that might result from the tuning process.) Please provide units and equations used.