> depends on resistance-per-meter
#10 AWG doesn't come in meters, it comes in Feet.
> For a cable run of 265', there is a voltage drop of 2.915V using 10 awg wire, correct?
I don't have the wacky AWG table memorized, but knowing a little about house wiring, that's in the ballpark.
But don't forget "regulation". The voltage at the load, 40V-3V= 37V, is so close to 40V (0.7dB) that the drop of volume is negligible. However 3V at 10 Amps is 0.3 ohms. Compared to a 4 ohm load, this is a Damping Factor of just over 10. Conventional Wisdom says that conventional speakers should be driven with very high Damping Factor, 40 or more.
This is similar to the house-wiring rule that even if a very long wire can safely carry the current, you never want more than 2% loss. Which actually is a "damping factor" of 50! If you violate this rule in house wiring, the lights flicker when the vacuum cleaner or sump-pump starts.
And if a conventional speaker is not well damped, it emphasizes its bass-resonances. Damping Factor of 10 can be 1dB bumps in the bass. For PA and background systems, no big deal. For precision monitoring, you want better.
You don't really need or want the "power" when computing line loss. You want the line resistance to be low compared to the load. For PA and other non-critical use, make line resistance up to 10% of speaker impedance. For critical work, use 2.5%. For low-pay one-shot events, you can go 20%, even 30%: the drop in power at the load is still small in dB, modern power amps have watts to spare, the 2dB-3dB bass-bumps may not be annoying, and can be EQ-ed away.
You can get in trouble if you go too far. I have some E-V PA speakers with a HUGE impedance rise in the bottom of the horn. A 3dB rise in the 800-2KHz area would be very annoying. (Actually: a 2-3dB drop everywhere the speaker is 8Ω, but it rises to 50Ω in the bass and the crossover.)
> Will all 400 watt amps have 56V at 8 ohms
I think you answered your own question. If you know the power and load, you know the voltage. We usually work in RMS-sine for audio amps, but the peak is 1.414 higher, and the peak-peak is 2.828 times higher.
And there are no perfect amplifiers. If you find the RMS voltage from power and load, multiply by 3 to get rounded-up peak-to-peak. The classic totem-pole output stage will have supply rails at least this high at full power: 56V RMS, 168V total rail voltage (usually +/-84V).
The no-load supply rails may be 20% to 50% higher than this. A 400W 8Ω amp probably idles with +/-110V rails.
> can the 'voltage gain' be multiplied by 'input sensitivity?'
SHould work; almost never comes out right. What is "input sensitivity"? Could be "for 1 Watt". Is often "for rated power (at low THD)". But
what you really need is "sensitivity to touch gross clipping", a topic they don't want to mention. The rated power is usually not much less than clipping power, but design and rating choices can make a big difference.
