Question

Using the string frequency equations when no tension in known, solve the following problem. You have a wire material that has a (volume) density of 7500 kg/m^3 and a yield stress of 0.43 MPa (1 MPa = 1 * 10^6 N/m^2). Find a combination of tension and a linear mass density of the wire that will cause the 1 m long wire to have a fundamental frequency of: 2 Hz 3 Hz 4 Hz without failing. In other words, at each fundamental frequency, based on equations 1 and 6. is there a combination of T and mu that ensures that the inequality of equation 6 is true? Record at least one combination for each fundamental frequency that works. If it is not possible, note that in your assignment.

Answer 1

For 2 Hz

=>   2 =   sqrt(T/u)/(2 * 1)

=>   sqrt(T/u) = 4

=> Tension = 4 N

=> linear mass density = 0.25 kg/m

For 3 Hz

=>   3 =   sqrt(T/u)/(2 * 1)

=>   sqrt(T/u) = 6

=> Tension = 6 N

=> linear mass density = 0.166 kg/m

For 4 Hz

=>   4 =   sqrt(T/u)/(2 * 1)

=>   sqrt(T/u) = 8

=> Tension = 8 N

=> linear mass density = 0.125 kg/m