Answer :
Final answer:
The tension in the A string of the violin is 68.2 N.
Explanation:
The prompt provides information about the fundamental frequency, length, and mass of the A string on a violin. We can use the formula for the fundamental frequency of a string, which is given by f = (1/2L) √(T/μ), where f is the frequency, L is the length of the string, T is the tension in the string, and μ is the linear density of the string.
We are given the frequency and length of the string, as well as its mass. To solve for the tension, we need to first find the linear density of the string, which is given by μ = m/L, where m is the mass of the string. Substituting the values, we get μ = 0.38 g / 0.28 m = 1.35 g/m.
Now we can solve for T using the formula for frequency, and substituting the values, we get 440 Hz = (1/2)(0.28 m) √(T/1.35 g/m). Solving for T, we get T = (4π²)(1.35 g/m)(440 Hz)²(0.28 m) = 68.2 N.
Therefore, the tension in the A string of the violin is 68.2 N.
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