No. Loudness is directly proportional to power delivery, not power requirement. What you’ve got in that headphone-centric efficiency rating of SPL/mW is requirement information, that doesn’t tell you how many existing amplifiers are going to satisfy that requirement.
I believe the “easy/hard to drive” question for the average consumer (or at least if I’m trying to give as helpful of an answer as possible) is about what result they can expect to obtain in practice, which means I can’t just look at the headphones, I also have to account for what source devices with what capabilities exist on the market at the moment of the discussion.
If the higher sensitivity transducer A has very low impedance and is at the extreme end of typical power delivery curves of sources on the market today (where mW output rolls off fast due to load impedance getting too low, resulting in current demand getting too high to be served without the amp burning up) - especially portable/pocketable ones - I want to tell the consumer they will have more trouble getting full loudness out of A with the real sources available to them in practice. Meanwhile B might have 32 ohms and be possible to push to high loudness by a vastly broader selection of the sources that can be bought today. So you could end up, paradoxically, with the higher sensitivity A being “harder to drive” in practice, because it would be harder to find all the right components to build a full audio chain that drives A properly.
It’s not a high probability scenario of course, since both the transducer and the DAC/amp side of the industry are constantly looking at what the other is doing and adapting their specs for new devices they’re putting on the market, but the point is you can’t be 100% sure of what result you’re going to get by looking only at the transducer-characterizing numbers like sensitivity or efficiency. There’s always a nonzero probability of getting into one of those marginal cases of bad power matching (especially on an evolving market, like the one recently evolving more toward lower impedance transducers than used to be the case), so in order to get reliably correct conclusions it’s best to always look at impedance too, and judge it vs. your prospective source’s capabilities of max current delivery (for low ohms) or max voltage delivery (for high ohms).
I don’t have a background in EE, so I guess that’s why I still have some difficulty wrapping my head around various aspects of Ohm’s Law. This article by a Taiwanese audio vendor summarizes many of my thoughts and views though on this topic. (And probably does a much better job of explaining it than I can!) And I think some of it may tie in pretty well with abm0’s comments above too.
It is a vendor though, so there’s a sales pitch embedded in the info as well, fyi. The writing on this is very good though, and pretty easy to understand I think.
Cam also did a video not too long ago on amps. So I’ll post that as well, for those who may have missed it. It goes too quickly for me to understand most of the concepts though. So this is probably better for those with a more advanced understanding of watts, volts, amperes, and ohms.
There’s also a brief article that goes with this as well here…
Last thing I’ll post is this Wikipedia article on headphone amps, which has some more general info that might be of use to some.
After reading the article by Archimago below, I may have to eat some of my previous words above re the DT770, since it appears that all three impedances of this headphone have a similar efficiency of around 96 dB/mW. And where they vary seems to be more in dB/V!
Exactly, because dB/V is not influenced by impedance, but dB/mW is. That’s why it’s also important to not call both of them “sensitivity”: they don’t even represent the same information.
Technically, the sensitivity of a system is how much output it produces in response to changing values of the “signal” or information-carrying input. For audio equipment, the “signal” is voltage variation. Every time-domain representation of an audio recording that looks like an oscilloscope reading going up and down symmetrically vs. a 0 level, that’s effectively a graph of the voltage that will be produced at the DAC output in order to pass that sonic information to the next device. Voltage variation is the information carrying phenomenon, not power delivery.
Meanwhile, the efficiency of a system is how much output it produces when fed what amount of input, most often using the same metric for both, like energy or power, and most often represented as a percentage: useful output vs. consumed input. But for audio since sound power doesn’t correspond very well to the human experience of different loudnesses, the convention was made to keep using sound pressure levels as the output metric (in dB SPL) but relate them to the electrical power consumed by the device (1 W for speaker specs, 1 mW for headphones).
This value depends both on the sensitivity and on the impedance at the same time, and you can’t tell from this one number if it’s being pushed to extreme values mostly by some extreme sensitivity or mostly by some extreme impedance, they’re mixed indistinctly here. You need additional specs to tell what’s causing some out of the ordinary efficiency value, like either dB/V or impedance. (P=V^2/R means between power, voltage and impedance you need to know two of them to calculate the third, you can’t get the full picture of what’s going on if you only know one of them.)
What you’ve got in that headphone-centric efficiency rating of SPL/mW is requirement information, that doesn’t tell you how many existing amplifiers are going to satisfy that requirement.
That’s why it’s also important to not call both of them “sensitivity”: they don’t even represent the same information.