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?

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.