A wire of length L is made up of two sections of two different materials connect

Question

A wire of length L is made up of two sections of two different materials connected in series. The first section of length

L1 = 16.6 m

is made of steel and the second section of length

L2 = 28.5 m

is made of silver. Both wires have the same radius of 5.45 ? 10?4 m. If the compound wire is subjected to a tension of 145 N, determine the time taken for a transverse pulse to move from one end of the wire to the other. The density of steel is 7.75 ? 103 kg/m3 and the density of silver is 1.05 ? 104 kg/m3.
__________ s

Explanation / Answer

since density=mass/volume

m1(steel)=d1xV1=d1L1x3.14xr12=7.75x103 x16.6x3.14x(5.45x10-4)2=0.12kg

m2(silver)=d2xV2=d2L2x3.14xr22=1.05x104x28.5x3.14x(5.45x10-4)2=0.279kg

v=sqrt(T/(m/L))=sqrt(145/(0.12+0.279)/(16.6+28.5))=sqrt(145/0.00885)=128m/s

V=S/t

t=s/V=L/v=45.1/128=0.352Sec

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