Let's take a simple example:
The DAC outputs 2 V for full-scale signals. The amps gain is 5x (about 14 dB). The headphone sensitivity is 95 dB @ 1 mW and nominal impedance 300 ohms. We want to listen at 75 dB SPL.
So the volume control needs to be set so that the amp outputs about 0.01 mW. To keep things simple let's take a full-scale pure tone (sine wave) as signal.
P = V*V/R
--> V = sqrt(P*R) = sqrt(0.00001 * 300) = 0.055 V
full-scale output: 2 V * 5 = 10 V
20*log10(0.055 / 10) = -45 dB ... or a voltage gain of 0.0055x and on a normal volume control that is somewhere around 8 o'clock so very close to the off position. That sucks.
Now let's assume you're listening to real music and the average* RMS amplitude of a track is -20 dB relative to a full-scale sine wave. Then we're at -25 dB (0.056x) which leaves plenty headroom for all the peaks that come close to full-scale. The volume control is still somewhere below 10 o'clock!
*) this needs to be a pretty dynamic song and the RMS amplitude can shortly hit -5 dB from time to time, which would be about 90 dB SPL. True peaks of course could reach 0 dB or even surpass that.
Compressed metal songs can reach an average of only -7 dB or even louder..
edit: lowered headphone sensitivity
Edited by xnor - 4/21/13 at 10:58am