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
- A740 N
- B370 N
- C1.48 10^6 N
- 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