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An aluminium wire is clamped at each end...

An aluminium wire is clamped at each end and under zero tension at room temperature. Reducing the tempreture, which results in a decrease in the wire's equilibrium length, increase the tension in the wire. What strain `((DeltaL//L))` rejults in a transverse wave speed of `100 m//s`? Take the cross-seectional area of the wire to be `5.00xx10^(-6)m^(2)`, the density to be `2.70xx10^(3)` kg//m^(3)`, and young's modulus to be `7.00xx10^(10)N//m^(2)`.

A

`3.86 xx10^(-4)`

B

`2.86xx10^(-4)`

C

`3.42xx10^(-4)`

D

`2.42xx10^(-4)`

Text Solution

Verified by Experts

The correct Answer is:
A

Young's modulus `Y= (T//A)/(Deltal //l), " "(Deltal )/(l ) = (T)/(YA)`
Wave speed `v = sqrt((T)/(mu))= sqrt((T)/(rho A))therefore T = rho AV^(2)`
`therefore (Delta l )/(l ) = (rho V^(2))/(Y) = (2.70xx10^(3) xx 10^(4))/(7.00 xx10^(10)) = 3.86 xx10^(-4)`
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