A steel wire hangs vertically from a fixed point, supporting a weight of 80 N at its lower end. The diameter of the wire is 0.50 mm and its length from the fixed point to the weight is 1.5 m. If the density of steel wire = 7.8 x 10^3 kg/m3, then what is the fundamental frequency emitted from the wire?
Correct answer: A. 76 Hz
- A. 76 Hz
- B. 176 Hz
- C. 50 Hz
- D. 150 Hz
Explanation
Tension acting on the wire is T = 80 N, length of wire from the fixed point to the weight is L = 1.5 m. We know, density of steel is ρ = 7800 kg/m³, so the linear mass density of steel wire, μ = ρ A = 7800 kg/m³ × π(0.50 × 10⁻³ m)²/4 m² = 1.53 × 10⁻³ kg/m.
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About Simple Harmonic Motion
Simple harmonic motion is oscillation in which acceleration is directly proportional to displacement and directed toward the equilibrium position. Work includes displacement, velocity, acceleration, phase, period, frequency, amplitude and energy, with applications to springs and simple pendulums. The restoring force and the conditions for SHM distinguish it from general periodic motion.
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