tomp wrote:

First you have to start with the difference between efficiency and sensitivity because these two terms are batted around as being the same and they are not. Efficiency is the ratio of acoustic watts produced by an input of electrical watts. Note that the absolute value of input power is not specified, just the ratio. Sensitivity is the acoustical power created by a speaker for an input of 2.83 volts.

Where did he value of 2.83 volts come from? It represents the voltage that when applied to an 8 ohm load results in an input power of 1 watt. The formula is W = Vsquared/ohms. Therefore 2.83 squared = 8.0089 divided by 8 is essentially 1. Here is the rub, Now days with most speakers having an impedance below 8 ohms the sensitivity figure looks better on paper than the efficiency figure. For example, if you have an 8 ohm driver with a sensitivity of 87 dB and a 4 ohm speaker with a sensitivity of 90 dB you could assume that the 4 ohm speaker is more efficient. Not so. remember that sensitivity is specified at 2.83 volts. That 2.83 volts on the 8 ohm speaker represents an input power of 1W. Looking at the formula, the square of the input voltage is the same 8.0089 for both speakers but that value divided by the 8 ohms yields 1W while the same value divided by the 4 ohms yields 2W. Therefore the 4 ohm speaker is drawing twice the power from the amp. Twice the power to the driver results in a 3 dB increase in output. So, in reality, despite the apparent higher "efficiency" of the 4 ohm driver, it has the same real efficiency as the 8 ohm driver. All of this has nothing to do with low frequency response.

Output SPL is a function of volume velocity. Since we are listening in a space that is not pressurized, we are talking about frequency response, not pressure response. In this condition, for a given SPL, for every octave decrease in frequency, the speaker must produce 4 times the volume. Note that this has nothing to do with diaphragm size. You can get volume displacement by any combination of cone size and cone excursion. There are some real tradeoffs but that is the physical basis of volume vs frequency. Note that I am now not talking about efficiency.

Now let’s move to efficiency. You can start throwing bricks at me now but the efficiency of a driver to reproduce a given SPL at a given frequency has nothing to do with only the diaphragm size. If that is the case why do modern small bass drivers seem to have lower efficiency than large drivers from the 50s? You have to remember Hoffman's Iron Law. There are three parameters you can juggle, low bass response, small box size, and high efficiency. Pick any two but you can't have all three at the same time. Back in the days when a 10 watt amplifier was big stuff, speaker designers had to design drivers with high efficiencies to get reasonable SPLs with that low level of input power. To do that they made two major compromises. First, they compressed whatever magnetic strength was available into a very short gap making the flux density very high which helped produce larger forces for a given current. But that short gap limited excursion forcing the use of larger diaphragms to get the required displacement.

Second, they made the total moving mass of the driver light to produce more excursion for a given force. That light moving mass required a very compliant suspension to achieve a low resonant frequency below which the bass rolled off. With the very high compliance of the suspension, the compliance of the box quickly became an important factor. Small box volumes actually would have lower compliance than the suspension of the driver, resulting in an increase of resonant frequency in the box with poor bass extension as a result. To avoid this, they went to large boxes which reduced the resistance (increased the compliance) of the air keeping the resonant frequency low. Today, refrigerator sized speakers are simply not selling. I won't go into the physical tradeoffs necessary to get low bass in a small box but suffice it to say that the efficiency takes it in the shorts.

As you can see the various design choices of the old larger drivers resulted in higher efficiencies, not just the diaphragm size. Add to this other devices to get more SPL at certain frequencies such as horn loading, tuned ports, passive radiators, etc. and actual efficiency can increase but at times with substantial acoustic tradeoffs resulting.

I know this is yet another of my very long explanations, but you can’t give a simple answer to driver performance. And this explanation just touches on the myriad of parameters and design compromises that happen every day in the building of any speaker. There were very smart people in the past that made excellent choices based on the state of the art back then and also many very smart people today that can take advantages of new materials, amplifiers, DSP and other things to produce a wide range of speakers for people with different needs. It is always about the compromises and making informed choices.