A copper wire is held at the two ends by rigid supports. At $30^{0} C$ , the wire just taut, with negligible tension. Find the speed of transverse waves in this wire at $10^{0} C$ (Young modulus of copper $= 1.3 \times 10^{11} N / m^{2}$ )
Co-efficient of linear expansion of copper $= 1.7 \times 10^{- 5} /^{0} c$
Density of copper $= 9 \times 10^{3} k g / m^{3}$

Question

Infinity Learn · Accepted Answer

$$Y=stressstrain$$ ⇒$$Y=F/A$$Δ$$l/l$$ ⇒$$Y=FlA$$Δl ⇒$$F=YA$$Δll Also, change in length due to temperature $$=$$ Δ$$l=$$αl∆θ $$F=YA$$α∆θ Speed of wave on string : $$V=F$$μ where μ$$=ml=A$$ρ ∴$$V=Y$$α∆θρ  $$=$$ $$1.3$$×$$1011$$×$$1.7$$×$$10$$−$$5$$×$$209$$×$$103$$ $$V=70$$ $$m/$$$$sec$$.

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A copper wire is held at the two ends by rigid supports. At 300C , the wire just taut, with negligible tension. Find the speed of transverse waves in this wire at 100C (Young modulus of copper =1.3×1011N/m2 )Co-efficient of linear expansion of copper =1.7×10−5/0cDensity of copper =9×103 kg/m3

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