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Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String

A wire of length 2.00 m is subjected to a tension of 160 N . Determine the linear mass density of the wire if its fundamental frequency of vibration is 100 Hz .

Options

  1. A1.0 10⁻³ kg/m
  2. B8.0 10⁻³ kg/m
  3. C2.0 10⁻³ kg/m
  4. D4.0 10⁻³ kg/m

Correct answer

A. 1.0 10⁻³ kg/m

Step-by-step solution

The fundamental frequency of a stretched wire is given by: f = 1 2L T where L is the length, T is the tension, and is the linear mass density. Rearranging the formula to solve for : = T (2Lf)^2 Substituting the given values L = 2.00 m , T = 160 N , and f = 100 Hz : = 160 (2 2.00 100)^2 = 160 (400)^2 = 160 160000 = 1.0 10⁻³ kg/m

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