Traverse E wave travel Time on wires

[Husker70]

Homework Statement

A 30.0m steel wire and a 20.0m copper wire, both with 1.00mm diameter,
are connected end to end and stretched to a Tension of 150N. How
long does it take a transverse e wave to travel the entire length of
the two wires?

Homework Equations

Voulume of Rod = pie r^2(L)
v = sqrrt T/mass per unit length
v = dt/dx

The Attempt at a Solution

I found the volume of the steel rod to be pie(.0001m)^2(30.0m) = 9.42x10^-7 m^3
I found the volume of the copper rod to be pie(.0001m)^2(20.0m) = 6.42x10^-7 m^3

I looked up the density of steel to be 7850 kg/m^3
I looked up the density of copper to be 8230 kg/m^3

The weight of steel rod should be 9.42x10^-7 m^3/7850 kg/m^3 = 1.2 x 10^-10 kg
Then divide by 30.0m = 4.0x10^-10 kg/m

The weight of copper rod should be 6.28 x 10^-7 m^3/8230 kg/m^3 = 7.63 x 10^-11 kg
Then divide by 20.0m = 3.82 x 10^-12 kg/m

Using V = sqrrt T/mass unit of length

Steel wire is sqrrt 150N/4.0 x 10^-12 kg/m = velocity of steel = 6.12 x 10^6 m/s
Copper wire is sqrrt 150N/3.82 x 10^-12 kg/m = velocity of copper = 3.93 x 10^13 m/s

I added them together amd divided by 2 to get an average of 1.97 x 10^13 m/s
across the whole wire. Then divided that number by 50.0m to get 3.93 x 10^11s

I know that isn't right as the answer is .329s
I'm not sure what I'm doing wrong. Any help would be appreciated.
Thanks,
Kevin

 

[Redbelly98]

That "shortcut" of averaging the two velocities is a common misconception, but wrong. Even if the wires were the same length!

How long does it take the wave to travel down the steel part?
How long does it take the wave to travel down the copper part?