for lossless transmission line, the wave number is:

k = i\omega\sqrt{LC} = i 2\pi/\lambda

replace the angular frequency with frequency and introduce a velocity factor

\lambda f = 1/\sqrt{LC} = v_f c

where c is speed of light. a typical coaxial transmission line has velocity factor about 0.79 for foamed polyethylene dielectric or 0.66 for solid polyethylene dielectric.

with the characteristic impedance 50 Ω, we can calculate the capacitance and inductance of the cable.

For 0.79 cable:

L = 211 nH , C = 84.44pF

for 0.66 cable:

L = 253 nH , C = 101.1pF

For 12.8MHz signal, the ¼-wavelength is 3.8645 meter for 0.66 cable and 4.6257meter for 0.79 cable.

with this data, a better simulation on the tuner box can be archived.