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

Answer

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

 $v_s = \sqrt{\dfrac{T}{\dfrac{m}{l}}}$

 $v_s = \sqrt{\dfrac{T}{\dfrac{\rho (Al)}{l}}}$

mass  =  density x volume

 $v_s = \sqrt{\dfrac{T}{\rho A}}$

 $v_s = \sqrt{\dfrac{T}{\rho \pi \dfrac{d^2}{4}}}$

 $v_s = \sqrt{\dfrac{134}{7860 \pi \dfrac{0.001^2}{4}}}$

v_s = 147.33 m/s

Speed of the wave of copper wire

 $v_c= \sqrt{\dfrac{T}{\rho \pi \dfrac{d^2}{4}}}$

 $v_c = \sqrt{\dfrac{134}{8920 \pi \dfrac{0.001^2}{4}}}$

v_c = 138.3 m/s

time required

 $t = t_1 + t_2$

 $t = \dfrac{l_s}{v_s} +\dfrac{l_c}{v_c}$

 $t = \dfrac{31}{147.33} +\dfrac{16}{138.3}$

t = 0.326