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

Answer Details

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.