The frequency of the first overtone can be calculated using the formula:
f = (1/2L)√(T/μ)
where L is the length of the string, T is the tension, and μ is the mass per unit length of the string.
In this case, μ = 2.90 g/108 cm = 0.0269 g/cm.
Therefore, the frequency of the first overtone is:
f = (1/2*70 cm)√(470 N/0.0269 g/cm) = 545.7 Hz
A guitar string is 108 cm long and has a mass of 2.90 g. From the bridge to the support post (L) is 70 cm, and the string is under a tension of 470 N. What is the frequency of the first overtone?
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