It's Simple

@kijanki

I’m not going to correct all your errors, but this the level math:

Assuming 0.02Ω in each cable lead [12’ of Belden 1311A or almost any equivalent gauge cable] with a 1V drive at the amplifier terminal:
4Ω: 4 / (2 x 0.02) = 0.990V across the speaker
8Ω: 8 / (2 x 0.02) = 0.995V across the speaker
db: 20 * log ( 0.990 / 0.995 ) = -0.043db

Doubling the lead resistance, +3 AWG numbers, only has 0.086db loss.

On a speaker with an impedance that varies from 4 to 16Ω, the total delta across the 20-20k is 0.13db or ±0.065db which is extremely difficult to hear on a dynamic signal.

Ian, your calculations are of course correct, and I would note for the record that Belden 1311A is AWG 12 (12 gauge) wire.

However as I'm sure you'll agree two of the expressions that were used in the calculations were not written correctly:

4Ω: 4 / (2 x 0.02) = 0.990V across the speaker
8Ω: 8 / (2 x 0.02) = 0.995V across the speaker

Should have been written as:

4Ω: 4 / (4 + (2 x 0.02)) = 0.990V across the speaker
8Ω: 8 / (8 + (2 x 0.02)) = 0.995V across the speaker

Best regards,
-- Al
 

Ieales, thank you for correction. I assumed gauge 17 (worst case) that is 0.1 ohm for total of 20ft, but calculated it wrong. The difference in level between 4 and 8 ohm speaker is 0.1dB. That’s most likely inaudible.

I kind of hate to bring this up, but there are obviously many variables besides L R and C involved with how cables sound, some of which I’ve alredy mentioned. There are also the variables of floor borne vibration and static electric charge, which is why cables should usually be suspended off the floor and why some sort of anti-static spray or device should be employed. A demagnetizer should be employed, making magnetism another variable. There are other variables, too, perhaps beyond scope. All of this, plus what others have posted, such as metal purity, etc, suggests that L R and C are not really the only game in town, as much as we might aspire to embrace mathematics and “classical electronics” as the end-all do-all for our hobby. It’s not nice to fool Mother Nature.

Kijanki, the calculation of a 6 db difference you provided in your post yesterday was correct, but it was for the wrong thing :-)

Note that in Ian's calculation there is also a 6 db difference between the 4 ohm situation and the 8 ohm situation -- the voltage drop **in the cable** of 10 millivolts vs. 5 millivolts!

Best regards,
-- Al