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Q.

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.

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Detailed Solution

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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