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

A piano wire weighing 6.00 g and having a length of 90.0 cm produces a fundamental frequency corresponding to "Middle C" ( = 261.63 Hz ). Determine the tension in the wire.

Options

  1. A740 N
  2. B370 N
  3. C1.48 10^6 N
  4. D1480 N

Correct answer

D. 1480 N

Step-by-step solution

Mass of the wire, m = 6.00 g = 6 10⁻³ kg Length of the wire, L = 90.0 cm = 0.9 m Fundamental frequency, = 261.63 Hz The fundamental frequency of a stretched string is given by: = 1 2L T where = m L is the linear mass density. Squaring both sides and rearranging for tension T : T = 4 L^2 ^2 = 4 L m ^2 Substituting the given values: T = 4 0.9 6 10⁻³ (261.63)^2 T = 0.0216 68450.26 T 1478.5 N Rounding off to three significant figures, we get: T = 1480 N

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