A steel wire of length 26.0 m and a copper wire of length 22.0 m, both with 1.00-mm diameters, are connected end to end and stretched to a tension of 170 N. During what time interval will a transverse wave travel the entire length of the two wires?

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ajeigbeibraheem ajeigbeibraheem · Answer 1 · 2020-03-29T06:03:22+02:00

Answer:

0.3189 s

Explanation:

The formula for calculating the speed of the wave in steel wire is:

[tex]v_s = \sqrt{\frac{T}{m/l}}[/tex]

[tex]v_s = \sqrt{\frac{T}{\frac{\rho(Al)}{l} } }[/tex]

[tex]v_s = \sqrt{\frac{T}{\frac{\rho \pi (d)}{2}^2 } }[/tex]

[tex]v_s = \sqrt{\frac{170N}{\frac{(7860 kg/m^3 \pi (1.00*10^{-3})}{2}^2 } }[/tex]

[tex]v_s =147 m/s[/tex]

The time required is:

[tex]t = t_1 + t_2[/tex]

= [tex]\frac{I_s}{v_s} + \frac{I_c}{v_c}[/tex]

= [tex]\frac{26.0m}{147 m/s} + \frac{22.0m}{154.9m/s}[/tex]

= 0.3189 s

Olajidey Olajidey · Answer 2 · 2020-03-29T06:08:48+02:00

Answer:

0.298s

Explanation:

Speed of wave in steel wire is

[tex]V_z = \sqrt{\frac{T}{m/L} }[/tex]

[tex]V_z = \sqrt{\frac{T}{ [\frac{p(Al)}{l}] } }[/tex]

[tex]V_z = \sqrt{\frac{T}{p\pi (\frac{d}{2})^2 } }[/tex]

[tex]V_z = \sqrt{\frac{170}{(7860)\pi (\frac{1\times 10^-^3 }{2})^2 } } \\\\= 166m/s[/tex]

Speed of wave in copper wire is

[tex]V_z = \sqrt{\frac{170}{(8920)\pi (\frac{1\times 10^-^3 }{2})^2 } } \\\\= 156m/s[/tex]

The time required is

[tex]t = t_1 + t_2\\t =\frac{l_z}{V_z} + \frac{l_z}{V_z}[/tex]

t = [tex]\frac{26}{166} + \frac{22}{155.77} \\\\= 0.298s[/tex]