The transmission line is divided into small units where the circuit elements can be lumped.
Assuming the resistance of the lines is zero, then the transmission line can be modeled as an LC ladder network with inductors in the series arms and the capacitors in the shunt arms.
The value of inductance and capacitance of each part determines the velocity of propagation of energy down the line.
Time taken for a wave to travel one unit length is equal to
T(s) = (LC)0.5
Velocity of the wave is equal to
v (m/s) = 1/T
Impedance at any point is equal to
Z = V (at any point)/I (at any point)
Z = (L/C)0.5
lumped.