The speed of a transverse wave, going on a wire having a length $$50$$ cm and mass $$5.0$$ kg, is $$80$$ $$m/s$$. The area of $$cross-section$$ of the wire is $$1.0$$ $$mm2$$ and its Young's modulus is $$16$$×$$1011N/m2$$. Find the extension of the wire over its natural length (in$$ $$mm).

Question

The speed of a transverse wave, going on a wire having a length $$50$$ cm and mass $$5.0$$ kg, is $$80$$ $$m/s$$. The area of $$cross-section$$ of the wire is $$1.0$$ $$mm2$$ and its Young's modulus is $$16$$×$$1011N/m2$$. Find the extension of the wire over its natural length (in$$ $$mm).

Infinity Learn · Accepted Answer

The linear mass density of the wire, μ$$=5$$×$$10$$−$$350$$×$$10$$−$$2=1.0$$×$$10$$−$$2kgmThe$$ wave speed is $$v=T$$μThus, the tension is $$T=$$μ$$v2=1.0$$×$$10$$−$$2$$×$$6400=64NThe$$ Young's modulus, $$Y=T/A$$Δ$$L/LThe$$ extension is, therefore, Δ$$L=TLAY=64$$×$$0.501.0$$×$$10$$−$$6$$×$$16$$×$$1011=0.02mm$$

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