From: DPierce@world.std.com (Richard d Pierce)
Subject: Re: Speaker efficiencies (was:  Re: Amp/speakers cut out -- Why?)
Organization: The World Public Access UNIX, Brookline, MA
Date: Thu, 10 Sep 1992 14:04:03 GMT

In article <1992Sep9.174140.27581@mnemosyne.cs.du.edu> trygve lode writes:
>
>In my main video system, I have a couple of VMPS ST-IIa/R speakers for the
>front speakers; the literature that came with them claims an efficiency of
>101 dB (1W/1M) (none of the drivers are horn-loaded) and a -3dB point at only 
>17 Hz.  Now, just for fun, I A/Bed them with a pair of B&W speakers that
>claimed an efficiency of 90 dB--and if there is a difference in the volume
>produced by these two pairs of speakers with 11 dB different claimed
>efficiencies, it was small enough to be hard to tell.  Further, the 
>Morel tweeters used in the VMPS speakers are only rated at 90 dB
>efficiency themselves, which suggests to me that it would be difficult 
>to design a speaker with 101 dB efficiency around them.
>
>So, how fast and loose do manufacturers play with specs like this?  Are
>there tests out there that actually give the results given?

Where VMPS if coming up with there 101 dB figure is a mystery to me. This
would suggest that the have a reference efficiency of somewhere in the
neighboorhood of 15-20%. This is approaching well designed narrow-band horns!

The efficiency and sensitivity of a system is something which is absolutely
constrained by the physics at hand. Again, without going into the nitty-gritty
details of the math, there are some very specifc and rigid releations between
the box size, the low-frequency cutoff, and the system's efficiency. The
relation looks something like so:

               3
     n0 = kn F3  Vb

where n0 is the "reference efficiency" (usually expressed in %), F3 is the
low frequency -3 dB point of the response (in Hz), Vb is the box volume (in
cubic meters, for this discussion), and kn is an "efficiency constant" whose
value depends upon the low frequency configuration, response factor, and so
on. The maximum values (presuming lossless enclosures and the selection of
the best, not necessarily flattest, response to get the highest possible
efficiency) are:

                  -6
    kn = 1.17 x 10     (for Qt = 1.2 closed box systems, gives about a 3 dB
                       bump in the bass)
                  -6
    kn = 2.34 x 10     (for maximally flat 4th order vented box systems)

These constants and the equation above represent what are refered to as the
"maximum efficiency/bandwidth/box volume" limits for enclosures. There are
many other configurations and thus constants (for example, a maximally flat
6th order system using 2nd order electronic equalization has a kn about twice
that of the 4th order system).

Now, to translate from efficiency to sensitivity requires a simple relation:

    Sens = 109 + 10 log(n0)

Where sensitivity is expressed as "dB SPL measured at 1 meter from the source,
with an electrical input of 1 watt)." This is the amount of sound pressure that
will be produced at the surface of a sphere with a radius of 1 meter by the
speaker. 109 dB is the amount of sound pressure produced on the surface of this
same sphere by an acoustical source radiating 1 watt. It might be more
realistic to consider the hemispherical efficiency, which is implicitly double
this, or 112 dB. 

But no matter, the point being that given any two of the troika of bandwidth,
box volume and efficiency, the third is easily derived knowing the
configuration of the system. Plug in some numbers from your spec sheet and see
how close you manufacturer's specifications come to physical reality. Most
reputable manufacturers are within a couple of dB, the difference being due
to normal production line variations, the actual details of the low-frequency
alignment, and so on. If the figure you get is more than, say 2-3 dB off, then
someone is lying or simply doesn't know what they're talking about. In some
cases, all three numbers (as in the example I gave in the previous article)
are simply made up on the spot.

.





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