A uniform wire of volumetric density 8000 kg m ⁻³ and Young's modulus 1.6 10¹¹ N m ⁻² is stretched such that its length increases by 0.2 % . The speed of transverse waves on this stretched wire is _____ m s ⁻¹ .

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Quantrex Academy · Accepted Answer

Correct answer: 200

Let the volumetric density be , Young's modulus be Y , and strain be . The percentage increase in length is 0.2 % , so the strain is: = L L = 0.2 100 = 0.002 According to Hooke's Law, the stress in the wire is: = Y = (1.6 10¹¹) 0.002 = 3.2 10^8 N m ⁻² The speed of a transverse wave on a stretched wire is given by: v = T Since tension T = A and linear mass density = A (where A is the cross-sectional area), we can write: v = A A = Substituting the values: v = 3.2 10^8 8000 = 40000 = 200 m s ⁻¹ Answer: 200

A uniform wire of volumetric density 8000 kg m ⁻³ and Young's modulus 1.6 10¹¹ N m ⁻² is stretched such that its length increases by 0.2 % . The speed of transverse waves on this stretched wire is _____ m s ⁻¹ .

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