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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a
70 m/sec
b
60 m/sec
c
40 m/sec
d
100 m/sec
answer is A.
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Detailed Solution
Y=stressstrain ⇒Y=F/AΔl/l ⇒Y=FlAΔl ⇒F=YAΔll Also, change in length due to temperature = Δl=αl∆θ F=YAα∆θ Speed of wave on string : V=Fμ where μ=ml=Aρ ∴V=Yα∆θρ = 1.3×1011×1.7×10−5×209×103 V=70 m/sec.