- 2070 Chaitra · 5 marks
Maximum wave speed in steel wire
Short answer
v_max = √(σ/ρ) = √(2.70×10⁸ / 7.89×10³) ≈ 1.85×10² m/s (185 m/s).
The elastic limit of steel forming a piece of wire is equal to 2.70×10⁸ Pa. What is the maximum speed at which transverse wave pulses can propagate along this wire without exceeding this stress? (density of steel = 7.89×10³ kg/m³)
Given: elastic limit (maximum stress) σ = 2.70 × 10⁸ Pa, density of steel ρ = 7.89 × 10³ kg/m³.
Formula. For a wire of cross-sectional area S, tension T = σS and linear density μ = ρS. The wave speed is
v = √(T/μ) = √(σ S / ρ S) = √(σ/ρ)
The area cancels, so the maximum speed depends only on the material.
Steps
- σ/ρ = 2.70 × 10⁸ / 7.89 × 10³ = 3.422 × 10⁴ m²/s².
- v_max = √(3.422 × 10⁴) = 185 m/s.
Answer: v_max ≈ 1.85 × 10² m/s (about 185 m/s).
✓ Answer checked by Claude Opus 5.5 (high effort)
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