I posted this in another thread, and I notice that there are quite a few people asking about it so I thought it might warrant a thread of it's own. I wrote all of this fairly quickly, and I'm not sure I understand all of the concepts perfectly. I know there are quite a few other people here who probably understand this beter than me, so correct me if I state anything incorrectly. I found pretty much all the other info I read on the subject to be accurate, but sometimes misleading.
Here is my explaination of why resistors help sound quality, and why lower impedance headphones are not always better:
The equations that we are concerned with should be:
V=voltage (potential difference) (volts)
P=power (proportional to volume)
So, as you can see there is an inverse relationship between current (I) and resistance (R). So for a given potential difference (voltage, V) which is provided by the DAP (digital audio player), the lower the resistance the more current will flow in the circuit. Also, power is proportional to volume, and as you can see by the second equation (with voltage (V) constant) the less resistance the greater volume. So with low impedance headphones you get more volume for a given voltage.
So, in theory you want low resistance (impedance) headphones to get greather volume output. But the problem is that many DAP's do not have a very powerful amp, and they run out of current. What happens is, there will be a bass note, and with low resistance headphones the volume of the bass note will start out at the correct volume and quickly drop off (possibly to zero). This happens so quickly you can't actually hear that this is happening, but results in the thinner, weak bass and overall 'tininess' (roll-off).
To get the best sound you need to use a resistor (or higher impedance headphones), so that the DAP's amp can provide plenty of current. BUT this will result in less current (and therefore volume) for a given voltage, so you will have to turn up the volume higher to get the same dB output. This results in faster battery drain (but as stated in other threads, this power usage is somewhat insignificant compared to backlight, drive spinning, etc).
For an ideal setup you will use a resistor and then you use a separate amp to increase the availabe current, and run that to your headphones.
You could also run the DAP's line out to the amp, and then (since the voltage is increased) you can get more volume with the resistor in place between the amp and headphones (or use high impedance headphones).
Hopefully this made sense (and is correct). I made an assumption that power is proportional to volume. We did a lab which proved power is proportional to brightness (in a light bulb), so I believe it would be the same for volume.
Also the power equation can be written in many different ways depending on what you substitute in:
All of these equations are equivalent, and are equivalent to the second equation above. I include these in case it makes it easier to see the relationship between voltage-resistance, voltage-current, current-resistance, depending on what you are looking to solve for. If you know the max current, voltage output of your DAP or amp you could theoretically find the best resistance to get max volume.
Also, check out this post and the links it contains (explains bass roll-off in DAP's):
this part written by ECE student:
this is a relatively simple definition of impedance. what was described here is mostly DC resistance.
impedance is in fact the vector sum of reactance (capacitive or inductive) and resistance in an AC circuit. I wont go into gruesome detail but you can get the idea from reading above.