A 25.0 steel wire and a 50.0 copper wire are attached end to end and stretched to a tension of 145 . Both wires have a radius of 0.450 . and their densities are 7.86 10 / for the steel and 8.92 10 / for the copper. (Note that these are mass densities, mass per unit volume, NOT linear mass densities, mass per unit length.) How long does a wave take to travel from one end to the other of the combination wire?

Respuesta :

Answer:

T= 0.45 sec

Explanation:

Given data:

length of steel wire = 25 m

length of copper wire is 50 m

tension = 145 N

STEEL AND COPPER WIRE diameter = 0.450

density of steel [tex]= 7.86\times 10^{3} kg/m3[/tex]

density of copper [tex]= 8.92\times 10^3 kg/m3[/tex]

we know that speed of waves is calculated as

[tex]V =\sqrt{\frac{T}{U}}[/tex]

[tex]U =  \rho \times A[/tex]

[tex]V_{STEEL} = \sqrt{\frac{145}{8.92\times 10^3 \times \pi (0.45\times 10^{-3})^2}}[/tex]  

[tex]V_{STEEL} = 160 m/s[/tex]

[tex]V_{copper} = \sqrt{\frac{145}{7.86\times 10^3 \times \pi (0.45\times 10^{-3})^2}}[/tex]

[tex]V_{copper} = 170 m/s[/tex]

time travel by wave from one end to other

[tex]=\frac{l_s}{v_s} + \frac{l_c}{v_c}[/tex]

[tex]= \frac{25}{160} + \frac{50}{170}[/tex]

T= 0.45 sec