The speed of a transverse wave, going on a wire having a length $$50$$ cm and mass $$5$$ g is $$80$$ $$m/s$$. The area of cross section of the wire is $$1.0$$ $$mm2$$ and its Young's modulus is $$8$$×$$1011N/m2$$. Find the extension in ×$$10$$−$$2$$ mm of the wire over its natural length.

Question

The speed of a transverse wave, going on a wire having a length $$50$$ cm and mass $$5$$ g is $$80$$ $$m/s$$. The area of cross section of the wire is $$1.0$$ $$mm2$$ and its Young's modulus is $$8$$×$$1011N/m2$$. Find the extension  in ×$$10$$−$$2$$ mm of the wire over its natural length.

Infinity Learn · Accepted Answer

The linear mass density isμ$$=5$$×$$10$$−$$3$$ $$kg50$$×$$10$$−$$2$$ $$m=1.0$$×$$10$$−$$2$$ kgmThe wave speed is $$v=F/$$μThus, the tension is $$F=$$μ$$v2=1.0$$×$$10$$−$$2$$ kgm×$$6400$$ $$m2s2=64$$ NYoung's modulus is given by $$Y=F/A$$Δ$$L/L$$.The extension is, therefore,Δ$$L=FLAY=64$$×$$0.501.0$$×$$10$$−$$6$$×$$8$$×$$1011=0.04$$ mm

Travelling wave

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The speed of a transverse wave, going on a wire having a length 50 cm and mass 5 g is 80 m/s. The area of cross section of the wire is 1.0 mm² and its Young's modulus is $8 \times 10^{11} N / m^{2}$ . Find the extension $(in \times 10^{- 2} mm)$ of the wire over its natural length.

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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 g is 80 m/s. The area of cross section of the wire is 1.0 mm2 and its Young's modulus is 8×1011N/m2. Find the extension in ×10−2 mm of the wire over its natural length.

The linear mass density isμ=5×10−3 kg50×10−2 m=1.0×10−2 kgmThe wave speed is v=F/μThus, the tension is F=μv2=1.0×10−2 kgm×6400 m2s2=64 NYoung's modulus is given by Y=F/AΔL/L.The extension is, therefore,ΔL=FLAY=64×0.501.0×10−6×8×1011=0.04 mm

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The speed of a transverse wave, going on a wire having a length 50 cm and mass 5 g is 80 m/s. The area of cross section of the wire is 1.0 mm² and its Young's modulus is $8 \times 10^{11} N / m^{2}$ . Find the extension $(in \times 10^{- 2} mm)$ of the wire over its natural length.