Impedance in headphones vs. speakers - confused

Ok. This is all starting to make sense to me now and I really appreciate your very clear and helpful answers. This has been bothering me for quite a while so it feels good to start to understand it :) Thanks!

Theres's only one thing that I still don't understand. Why is it that an iPod or iPhone won't get stressed out delivering the current required for 32 ohm headphones (apple earbud's or a pair of Grado's for example) but my $3000 integrated amplifier which requires a minimum of 50 ohms has a problem with it? Yet the integrated amp can apparently supply enough current to power 4 ohm home speakers with no problem.

Excellent explanations by Bombaywalla.

A couple of additional points:

1)Another possible reason for the recommendation by your integrated amp manufacturer to use headphones having impedances of 50 ohms or more is that while its headphone amplifier circuit might have no trouble providing the voltage, current, or power required by low impedance headphones, its output impedance may be too high, and vary too much as a function of frequency, to provide good sonics when driving low impedances. That same problem sometimes arises in interfacing preamp outputs to power amp inputs.

If the headphone amp within the integrated amplifier has an output impedance that is a substantial fraction of the impedance of the headphones, and if that output impedance varies significantly over the audible frequency range (as may often be the case), the resulting frequency response will be significantly non-flat, as a result of the voltage divider effect. The voltage that the headphone amp "tries" to put out being divided between the headphone's impedance and its own output impedance. For a given output impedance, the higher the impedance of the headphones the less significant that effect will become.

2)Keep in mind that to produce a given volume level at the listener's ears, the power required by a set of headphones is VASTLY less than the amount of power required by a pair of speakers. Perhaps 100,000 times less, or thereabouts. Headphones commonly produce sound pressure levels of around 100 db in response to an input of 1 milliwatt (0.001 watts). Speakers having typical efficiencies that are listened to at typical distances will require, as a rough order of magnitude, something like 100 watts to produce that same spl.

So a hypothetical 32 ohm speaker, were such a thing to exist, would require vastly more current, voltage, and power to produce a given volume at the listener's ears than a 32 ohm headphone.

Regards,
-- Al

Theres's only one thing that I still don't understand. Why is it that an iPod or iPhone won't get stressed out delivering the current required for 32 ohm headphones (apple earbud's or a pair of Grado's for example) but my $3000 integrated amplifier which requires a minimum of 50 ohms has a problem with it? Yet the integrated amp can apparently supply enough current to power 4 ohm home speakers with no problem.

The electronics for the integrated amp to drive 4 Ohm speakers should be totally different & separate from the electronics that is the headamp. There should be 2 separate circuit boards for these 2 separate functions. The electronics that is driving your 4 Ohm loudspeaker is NOT the circuit driving your headphone. Once you have switched off your int. amp & let is sit for several hours to let the power supply caps discharge, pop open the top lid & take a look inside. You should see a separate circuit board for the headamp.
All the money was spent in making a much better int amp to drive a loudspeaker than a headamp to drive headphones. The headamp was thrown in there as a feature with minimal cost & effort. People who are serious about headphone listening more often than not have a dedicated/separate headphone amp.

Nadman12

Power delivered to headphones P=U^2/R, therefore in order to keep the same power/loudness, with higher impedance headphones, output voltage has to be also higher. Loudness becomes limited either by gain that is too low (tailored for common lower impedance earphones) or supply voltage (that is low in battery operated devices) - whatever occurs first.

Same exists for the speakers but in order to deliver more power (especially with SS amps) speakers are low impedance hence amp has to be able to deliver more current (since power is also P=I^2*R) and sometimes reaches amp's current limit.

I really appreciate all the help! Thanks everyone!