First of all, low impedance means nothing when it comes to power requirements. A headphone at a low impedance could be extremely hard for an amplifier to power, or it could be easy. All the impedance determines is the amount of voltage vs. current needed to develop a certain power level. That power level determines sound pressure level (loudness), given the headphone's
efficiency (or
sensitivity in some quarters).
So, the power required by a headphone is completely dependent on its sound pressure efficiency (sensitivity) and completely independent of impedance, period.
The only reason - the ONLY reason - impedance enters into a power discussion, is because it determines what proportion of power vector quantities (current and voltage) that the amplifier must produce. Some amplifiers can produce current more easily than voltage (solid-state, battery-powered portables, etc.). Other amplifiers can produce voltage more easily than current (tubes, desktop amps with mains-supplied power supplies). Typically, small solid-state devices such as smart phones, small DAPs, etc., are only powered by batteries. That means their ability to produce voltage is limited.
Low impedance headphones need more current than voltage for a given power level (Ohm's law), whereas high impedance headphones need more voltage than current. Consequently, small telephones, DAPs and portable amps can power low impedance headphones more easily because they are not required to produce much voltage.
However, as stated above - the power level itself is completely dictated by the headphone's efficiency, period.
Another misconception - Despite many objectivist's opinion, a statement such as "some amps not only amp they also make the sound quality better"
is entirely true. Why is this? Because every headphone needs an amplifier of some sort - it doesn't matter what the device. The problem is, many amplifiers that are built into small portable devices, smart phones or sound cards - such that you don't even think of the fact that there really is an amplifier in there - will lead to a predictable reaction once a high-quality amp is inserted into the headphone audio string: "it actually makes the sound quality better." This is because the lack of power or lack of proper control over the headphone drivers, probably means the sound quality was cr*p from the beginning and the power level the headphones desired was sub-standard all along.
People know what they hear, even if the terms they use to describe it offend the more technically oriented. Opinions such as those shouldn't be discounted as inaccurate, simply because they're non-technical.
