Question

A steel wire of length 31.0 m and a copper wire of length 16.0 m, both with 1.00-mm diameters, are connected end to end and stretched to a tension of 134 N. During what time interval will a transverse wave travel the entire length of the two wires? (The density of steel and copper are 7860 and 8920 kg/m3, respectively.) .4 Incorrect: Your answer is incorrect.

Answer 1

given,

steel wire length = 31 m

copper wire length = 16 m

diameter of both the wire = 1 mm = 0.001 m

Tension = 134 N

Density of steel = 7860 kg/m³

Density of copper = 8920 kg/m³

Speed of the wave of steel wire

`v_s = \sqrt{(T)/((m)/(l))}`

`v_s = \sqrt{(T)/((\rho (Al))/(l))}`

mass = density x volume

`v_s = \sqrt{(T)/(\rho A)}`

`v_s = \sqrt{(T)/(\rho \pi (d^2)/(4))}`

`v_s = \sqrt{(134)/(7860 \pi (0.001^2)/(4))}`

v_s = 147.33 m/s

Speed of the wave of copper wire

`v_c= \sqrt{(T)/(\rho \pi (d^2)/(4))}`

`v_c = \sqrt{(134)/(8920 \pi (0.001^2)/(4))}`

v_c = 138.3 m/s

time required

`t = t_1 + t_2`

`t = (l_s)/(v_s) +(l_c)/(v_c)`

`t = (31)/(147.33) +(16)/(138.3)`

t = 0.326