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$$L=TLAY=64$$×$$0.501.0$$×$$10$$−$$6$$×$$16$$×$$1011=0.02mm$$

Travelling wave

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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 $16 \times 10^{11} N / m^{2}$ . Find the extension of the wire over its natural length (in mm).

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Travelling wave

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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).

The linear mass density of the wire, μ=5×10−350×10−2=1.0×10−2kgmThe wave speed is v=TμThus, the tension is T=μv2=1.0×10−2×6400=64NThe Young's modulus, Y=T/AΔL/LThe extension is, therefore, ΔL=TLAY=64×0.501.0×10−6×16×1011=0.02mm

Ready to Test Your Skills?

free study material

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 $16 \times 10^{11} N / m^{2}$ . Find the extension of the wire over its natural length (in mm).