A copper wire is held between rigid supports. At 30°C it is just taut, so take the initial tension as negligible. Find the transverse-wave speed at 10°C. Given Y = 1.3 × 10¹¹ N m⁻², α = 1.7 × 10⁻⁵ °C⁻¹ and ρ = 9 × 10³ kg m⁻³.
Physics · Wave Motion
JEE Mains Practice

Question

A copper wire is held between rigid supports. At 30°C it is just taut, so take the initial tension as negligible. Find the transverse-wave speed at 10°C. Given Y = 1.3 × 10¹¹ N m⁻², α = 1.7 × 10⁻⁵ °C⁻¹ and ρ = 9 × 10³ kg m⁻³.

Physics · Wave Motion

G1 Physics · Accepted Answer

Step 1: Cooling by ΔT=20°C while ends are fixed creates stress σ=YαΔT. Step 2: Transverse-wave speed v=√(σ/ρ)=√(YαΔT/ρ). Step 3: v=√[(1.3×10¹¹)(1.7×10⁻⁵)(20)/(9×10³)]≈70 m s⁻¹.