> How does one discover the impedance of a pair of headphones? My understanding is that, at least on loudspeakers, the impedance varies depending on frequency, so it can't be as simple as connecting an ohmmeter... eh, right?
Eh, right. Speakers or headphones, measure the DC resistance, round up, call it the impedance.
Yes, it varies with frequency. But we mostly care how low it goes, not how high it goes. And for broadband transducers, the motional impedance is very low except in narrow bands like bass resonance. That motional impedance (outside resonant zones) runs 2Ω-0.1Ω. The coil has an inductance that will raise impedance at the top of the band, but rarely a whole lot and not at frequencies we make big power. So what you see looking into speakers or headphones is some very low impedance in series with the Copper Resistance, which you measure with an ohm meter.
"8Ω" speakers will show 6Ω or 7Ω DCR: speakers need to be somewhat efficient. Between the bass resonance and the treble inductance, impedance won't dip lower than 8Ω or 7Ω or so, and is higher over most of the band.
Headphones measuring 28Ω DCR will be around 300Ω over most of the audio band, with a 600Ω peak at resonance and rising to 450Ω at 20KHz. 300Ω near-enough.
You can get in trouble with VERY efficient speakers. 1930s theater horns approach 50% power efficiency, which means their motional impedance is similar to their electrical impedance, and the best will do this over much of their working bandwidth. JBL 2440 measures 12Ω DCR, is rated 16Ω, but in a BIG well designed horn (not a little 800Hz sectoral) it will be above 20Ω from ~200Hz to over 1KHz.
You can get in trouble with crossovers. A designer trying to fix a crossover suck-out may turn to high-Q crossover filters. Power can not be created, but the high-Q filters will transform 8Ω drivers to much lower impedance which will draw more power out of the amplifier. There are cases of "8Ω" speakers showing 3Ω at crossover. OTOH, I have some E-Vs with very efficient tweeters and to tame them, EV used a no-Q crossover that rises to 50Ω at 2KHz. Not a problem for typical stage amps, but could be piercing with some low damping audiophile amps.
Yeah, use the ohm meter. It is rarely far off.
Some digital ohm meters do not like odd loads. If in doubt, wire a 9V battery and a 900Ω resistor in series with the speaker, measure the DC on the speaker, do the math. 0.1V is 10Ω, near enough.