Lets imagine we have amplifier with 2 ohm output impedance connected to 8 ohm impedance load, headphone for example. Becose the amp impedance is 2 and headphone is 8, then the damping factor is 4.
How will the cable affect our system? If the cable has 2 ohm resistance, does it add up to the source impedance and decrease damping factor from 4 to 2 becose 2 ohm source + 2 ohm cable = 4 ohm output impedance divides 8 ohm load = 2x damping factor.
Or does it add to the load impedance and increase the damping factor becose 8 ohm headphone + 2 ohm cable = 10 ohm load divided 2 ohm amp output impedance = 5x damping factor?
My understanding (after 2 decades of RF design) is:
The characteristic impedance, Z0, of a transmission line, such as coaxial cable, is a notional concept that relates the current flowing through the line with the voltage across it. Heaviside and later Maxwell showed that a transmission line can be considered as a concatenation of short RLGC sections (series R and L, shunt G and C) and Z0 is given by
Z0 = sqrt((R+j*w*L)/(G+j*w*C))
where j = sqrt(-1)
w = 2*pi*frequency (omega)
and R,L,G,C are per unit length
For practical cables made from good conductors and good insulators the physical values of the R,L,G,C work out mean that for f>100kHz, say, Z0 ~= (sqrt(L/C))
Thus at HF the char. impedance is real and fairly constant.
At medium and audio freq. it is complex and varying.
with RG-58
R = 39mOhm/m
L = 250nH/m
C = 100pF/m
At f> 250kHz, j*w*L ~= 10*R and Z0 is quite constant 50Ohm.
At audio frequencies therefore the char. impedance is complex and a function of freq (i.e. Z0(f))
But what is the effect of this impedance? Modeled as a two port:
https://en.wikipedia.org/wiki/Transmission_lineThen using ABCD parameters, you will probably be able to see how the output inpedance of the amplifier (Port 1) is transformed via
https://en.wikipedia.org/wiki/Two-port_networkto V1, I1 = ABCD V2, I2
and so see how much of an effect your tx line has. It's not a simple resitive addition, as the shunt capacitance is usually non negliable.
This will give you an effective Zsource that is connected to your load.
But Zsource is a function of freq. (due to the tx line) and because your amplifier will have a damping factor (output impedance) that rises with freq.
So... basically, IMO damping factor is just a fairly meaningless marketing term (which is is freq. dependent). Your speaker network as funkloads of resonances, and will be 8Ohm restive at 1 single point probably and unless you are using very long (say >5m) lines the tx line's characteristics are not interesting to consider, and cannot be regarded as a simple resistance in any case.