A steel wire of length 0.50m is stretched between two fixed points and its fundamental frequency is 200Hz. The speed of the wave in the wire is

The speed of a wave in a stretched string is given by the formula v = √(F/μ), where v is the speed of the wave, F is the tension in the string, and μ is the linear mass density of the string (mass per unit length). The fundamental frequency of a stretched string is given by the formula f = (1/2L)√(F/μ), where L is the length of the string. In this question, we are given the length of the steel wire (L = 0.50m) and its fundamental frequency (f = 200Hz). We are asked to find the speed of the wave in the wire. Using the formula for the fundamental frequency, we can rearrange it to find the tension in the string: F = (4L^2μf^2) Substituting this expression for F into the formula for the wave speed, we get: v = √((4L^2μf^2)/μ) v = 2Lf Substituting the values given in the question, we get: v = 2(0.50m)(200Hz) = 200m/s Therefore, the speed of the wave in the wire is 200 m/s. The correct option is (c): 200ms^-1.