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The speed of a transverse wave going on...

The speed of a transverse wave going on a wire having a length 50 cm and maas 5.0 g is `80ms^(-1)` The area of cross section of the wire is `1.0mm.^2` and its Young modulus is `16 xx 10^(11) N m^(-2).` Find the extension of the wire over its natural lenth.

Text Solution

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The linear mass density is `mu=(5xx10^(-3)kg)/(50xx10^(-3)m)=1.0xx10^(-2) kg//m`
The wave speed is `v=sqrt(F)//(mu)`
Thus, the tension is `F=muv^(2)=(1.0xx10^(-2)(kg)/(m))xx6400(m^(2))/(s^(2))=64 N`
young's modulus is given by `Y=(F//A)/(DeltaL//L)`
The extension is, therefore,
`DeltaL=(FL)/(AY)=(64xx0.50)/((1.0xx10^(6))xx(8xx10^(11)))=0.04 mm`
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