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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^(-2)m) = 1.0 xx 10^(-2) kgm^(-1)`
The wave speed is `upsilon = sqrt(F//mu).`
Thus, the tension is `F = muupsilon^2`
`=((1.0 xx 10^(-2)kg m^(-1)))xx6400 m^2 s^(-2) = 64 N.`
The Young moddulus is given by
`Y = (F//A)/( DeltaL//L)`
The extension is, therefore,
`DeltaL = (FL)/(AY)`
`=((64N) (0.50m))/((1.0xx 10^(-6) m^2)xx (16xx10^(11) N m^(-2)) = 0.02 mm.`
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