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

a) v   = sqrt(T /u )
T - tension in the string
u - linear density .
cross section area A = pi*r^2 = pi x (5.45 x 10-4)^2 = 9.33 x 10-7
linear density of steel u1 = 7.75 x 10^3 *A = 7.23 x 10-3kg / m
linear density of silver u2 = 1.05 x 10^4 *A =   9.8 x 10-3kg/m

speed in steel wire v1= sqrt(145 / 7.23x10-3 ) = 141.62 m/s
speed in silver wire = sqrt(145 / 9.8x10-3) = 121.64 m/s

time =d/v
total time = 16.6 / 141.62    +   28.5 / 121.64   = 0.352 sec

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