Measuring and matching audio output impedance?

[switchabl]

In other words, why do some of these headphone amps have switches for low and high output impedance?  Why wouldn't 'low' work for everything?

This is a very good question.  IMO the correct answer is that low impedance does work for everything.   However, anytime there is an audible difference between two configurations, there will always be some that prefer the technically worse choice.  So if high impedance sounds different, someone will like it that way.

http://nwavguy.blogspot.com/2011/02/headphone-amp-impedance.html

This, basically (btw, that blog has a lot of good info on audio design).

Also, once upon a time... when amplifiers all used vacuum tubes, it was hard to get low output impedance. So, in order to optimize power transfer, it was actually common to have matched audio connections (input impedance = output impedance = 600 ohm). Headphones had 600 ohm impedance as well and could just be plugged into a normal line output. Those systems have been obsolete for a long, long time. But I guess it is still at the back of people's minds, so you always get someone saying "aren't headphones supposed to be impedance matched?".

[TimFox]

A vacuum-tube amplifier transformer coupled to a loudspeaker or medium-impedance headphone is designed to drive that impedance, but its actual source impedance does not equal the optimal load impedance.
Audio-generator test equipment, in order to have a defined impedance, usually has a physical resistor after a low-impedance output (usually into a matched attenuator) to have a 600 ohm output impedance.
Such equipment can be used to drive a high impedance or matched 600 ohm impedance, or even a lower impedance, where the known 600 ohm output impedance allows you to calculate the voltage across the load.
Equipment designed to drive very long twisted-pair audio transmission lines (like telephone trunk lines) often did the same thing in order to double-terminate the transmission line.

[radiolistener]

Sure you are supplying less electrical power but how much is converted into acoustic power? I think that's the point switchabl is making. That although the impedance is lower, you usually have higher sensitivity (which I'm assuming is directly related to efficiency of electrical to acoustic power conversion).

Power consumed by headphones is transformed into energy of acoustic waves. In other words - more power consumed by headphones lead to more powerful sound. Of course, some fraction of power will be loss for heating, but that part is relative to a total power and that fraction will be about the same for both - matched and non matched connection (on a high frequency with a small wavelength it may be different due to HF energy accumulation and amplitude grow). Since headphones with matched connection consume higher power, they put more energy into acoustic waves.

It means that headphones connected with impedance match is more sensitive and produce more loud sound than one connected with impedance mismatch.

The reason why low impedance headphones are named "more sensitive" is because their impedance is better matched with low impedance output of amplifiers. But if their impedance will be too low for amplifier (much smaller than amplifier impedance), they will loss their sensitivity the same as high impedance headphones... 

This is because the best power transfer efficiency happens when power source and power load impedances are the same. So the best headphones sensitivity happens when their impedance is equal to amplifier impedance.

But since headphone power is too small, their sensitivity is not critical parameter, because you can easily set up higher sound volume on your amplifier in order to compensate headphones sensitivity. It will be critical for a high power speakers, because if you attach high impedance speakers to a low impedance amplifier (or low impedance speakers to a high impedance amplifier), it will lead to a high power loss and it may even damage your amplifier.

[Peabody]

I spent some time at Guitar Center trying out their headphones.  The only ones that were big enough for my ears were the Sennheiser HD280s, but they pressed too hard against my head, and were quite uncomfortable.  The AKG K240s were nowhere near big enough.  Well, better to find out that way than after buying them.

So it looks like I'll be using some kind of in-ear monitors.  I'm still a bit perplexed by my experience with the 7Hz Zeros.  I watched all the reviews of them again, and what I heard was nothing like what they described, or what the graphs showed.  And that wasn't just on the piano.  I also tested them on my computer, my MP3 player, and my stereo system, and they sounded like Rice Krispies on all sources, whereas my cheap MP3 player earbuds sounded ok on all.  But if something was defective, how would that affect both sides?  So it's a mystery.

I did order the headphone amp module from Amazon.  It was only $5.50, and could be fun to play with even if I don't end up needing it.

[Yuu]

The reason why low impedance headphones are named "more sensitive" is because their impedance is better matched with low impedance output of amplifiers. But if their impedance will be too low for amplifier (much smaller than amplifier impedance), they will loss their sensitivity the same as high impedance headphones... 

Hmmm, are you sure? If I look up headphone sensitivity, the definition is something like "decibels of sound pressure level per milliwatt." This sounds to me like a useful characterization of transducer efficiency and not a marketing gimmick. If it was a marketing gimmick then all that would matter to characterize the headphones would be headphone impedance as a function of frequency. Maybe it's the case sensitivity ends up being somewhat an irrelevant factor compared to impedance matching? Just curious