When this is true, the 4 Ohm is usually 3 dB more sensitive. The low impedance causes extra current flow which provides for increased force against the same magnet.
This seems to require clarification!
Given two drivers of the same **efficiency** (1 watt, 1 meter), if one is 8 ohms and the other is 4, the 4 ohm unit will be 3 db more **sensitive** (sensitivity is measured at 2.83Volts at 1 meter; if this is 8 ohms that is one watt, at 4 ohms its two watts; two watts is double one watt and there is your 3 db ).
That current will not flow as expected by the speaker designer if the amplifier output impedance is higher than about zero ohms. This is because as the output impedance is increased, more and more power will be dissipated in the output section of the amp rather than the load- dissipated in the form of heat.
That’s a lot of amps! In particular, this is especially true of tube amps, whose output impedance can often be measured in ohms rather than fractions of an ohm. One might ask, ’what is the point of such an amplifier?’ and the answer has to do with how humans perceive sound.
In a nutshell, we perceive volume, or sound pressure, by listening for the higher-ordered harmonics. This is because pure tones do not exist in nature, and apparently nature sorted out millions of years ago that listening for the higher-ordered harmonics is more expedient, as it would millions of years before anyone invented pure fundamental tones :)
BTW this is very easy to prove with simple test equipment and is not a matter of debate. I’ve posted the way to prove this a number of times on this site.
Since this is the case, a good number of designers (myself included) prefer to design amps that by intention do not make the higher ordered harmonics. To do this often requires a higher output impedance, because to do that means avoiding loop negative feedback (which is known to enhance higher orders and generate more of them at the same time; see Norman Crowhurst). Loop feedback lowers output impedance; without it the output impedance is therefore higher.
It also happens that it is far easier to design such an amplifier by avoiding the use of semiconductors in the signal path. Semiconductors have non-linear capacitive elements inherent in their junctions (magnified by current through the junction) and these are known to create higher ordered harmonics in the distortion structure of the device (FETs and MOSFETs far less so than conventional bipolar devices; a particular device known as a varactor takes advantage of this aspect and is used as a variable capacitance to tune radio receivers).
The bottom line is that if you are dealing with an amplifier designed to not make higher ordered harmonics (as opposed to just low THD in general), the usual voltage rules as defined in the quote above simply don’t work (and I explained why in my second paragraph). Put another way as a speaker designer you have to pay attention to driver efficiency rather than sensitivity.
This is why back in the old days, many speakers had mid and tweeter level controls. They were not there to adjust the speaker to the room, they were there to adjust the speaker to an amplifier of unknown voltage response (high output impedance).
The approach is trickier, but has the advantage of less overall audible distortion (which the ear converts to tonality, often favoring that tonality over actual frequency response errors!).
In most cases this design approach is to avoid ’brightness’ and ’harshness’; two audiophile terms used to describe the presence of trace amounts of higher ordered harmonic distortion.
The way I see it, if a system **always** has brightness (which will be found to not be toned down by a treble control because it does not arise from a frequency response error) then the best it will sound will be like a nice stereo rather than real music.
Again, this all comes down to intention. Is your intention to get the system to sound as good as it can or is it more important to simply play loudly? If the former, than some of the lower impedance speakers and higher power transistor amps will be of interest; if the former, then you will be very careful to be matching the speaker to the amplifier (and not the other way ’round) and most likely avoiding lower impedances in general.