What is the mass of a string that is 17 cm long and has a fundamental frequency of 792 Hz when under a tension of 1.7 kN?
Question
What is the mass of a string that is 17 cm long and has a fundamental frequency of 792 Hz when under a tension of 1.7 kN?
Solution
To solve this problem, we need to use the formula for the fundamental frequency of a vibrating string, which is:
f = (1/2L) * sqrt(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 (mass/length) of the string.
We are asked to find the mass of the string, so we need to solve this equation for μ (which is equal to mass/length), and then multiply by the length to get the mass.
Rearranging the formula to solve for μ gives:
μ = T / (4L²f²)
Substituting the given values (converting lengths from cm to m and tension from kN to N):
μ = 1700 N / (4 * (0.17 m)² * (792 Hz)²)
Calculate the value of μ, then multiply by the length of the string (in meters) to find the mass.
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