Wave reflection and transmission between two ropes with different densities

[masterchiefo]

Homework Statement

An incident wave frequency f =500Hz , power Wi = 50 W and amplitude Ai= 5 mm spreads to the positive x in a linear density rope u₁ unknown. When the wave encounters another rope ( attached to the first at a point P) density linear u₂= 64 g/m (such as u₂>u₁ ) , The transmitted wave has a power Wt = 32 Watts.

a) Determine u₁, and the value of the impedance Z₁ and Z₂.

Homework Equations

The Attempt at a Solution

64g/m = 0.064kg/m
5 mm = 0.005 m

T = Wt/Wi
T= 32/50
T = 0.64

R + T = 1 => R + 0.64 = 1
R = 0.36
R = r²
0.36 = r²
r = 0.6

Ar = r*Ai
Ar = 0.6 * 0.005
Ar = 0.003

sqrt(u₁)/sqrt(u₂) = (Ai + Ar)/ (Ai - Ar)
sqrt(u₁)/sqrt(0.064) = (0.005 + 0.003)/ (0.005 - 0.003)
u1 = 0.1024

Something is wrong and I can't figure it out, I know its wrong because it says u2 has to be bigger than u1, and my answer of u1 is bigger than u2.

thanks.

 

[Simon Bridge]

Show your reasoning at each stage in the calculation.

 

[masterchiefo]

I resolved this problem, I do not need help.

 

[Simon Bridge]

You can help others if you show how you solved the problem.