On Wed, 08 Apr 2009 17:11:00 +0100, Jim Lesurf
wrote:

In article 49f6beb7.178501281@localhost, Don Pearce
wrote:
On Wed, 8 Apr 2009 15:56:08 +0100, "Keith G"
wrote:

The phrase "They are very efficient - in a cabinet, the PM7 hits over
103dB/watt." comes up.

Now, this has always mystified me, especially since I asked an 'expert'
at a famous (but fairly recently changed hands) 'speaker company'
about this very thing and he didn't think the sensitivity of a speaker
(Fostex in the Buschhorn cabinet, at the time) could be changed
(increased *or* decreased) by the enclosure it was used in! So, who is
right here? (Makers claim for the PM7A is a sensitivity of 96 dB at
1m/1kHz/1 watt...)


Dead right. The efficiency of a speaker is built into the driver when it
is designed. I guess you have heard of the Thiele Small parameters; they
describe the sizes, masses, springiness, damping - all the things that
the designer will choose when he specifies his speaker. Anyway,
efficiency can be calculated straight from a couple of those parameters
(can't remember which right now).

I have my doubts that is the entire story. For a speaker unit in free space
the acoustic coupling between the cone/piston movement and the air will
vary with frequency. The electromechanical efficiency will tell you how
much cone displacement you get for a given electrical signal. IIRC over a
fair range speakers tend to be mass-limited where the wavelength isn't tiny
compared with the cone scale-size.

Nothing is ever the entire story, but all I have done so far with
speakers suggests that as a first approximation it seems to work out.

But then there is the question of how much air pressure variation you
radiate for a given cone displacement/velocity. This also affects the
efficiency.

Thus if you fit a baffle you can prevent air movement being 'short
circuited' around the speaker unit and get larger pressure variations.
Hence - potentially - higher overall efficiency. Unless the pressure rise
simply reduces the movement to compensate exactly. But is that the case if
the speaker movements are mass controlled?


I think we can assume mass control - which is true for the majority of
the operating range. But compliance control is what you use to
calculate the dimensions of the box. at Fs.

In practice also the efficency may improve if judged in terms of *volts* in
if the change in arrangement drops the impedance. So values quoted in terms
of presuming a given drive *voltage* may not be the same as those based on
the power power into the coil.

Anyway lets start with return springs. There are two. The first most
obvious one is the rubber suspension and it's easy to see how that
works. You end up with a spring and mass (the cone) which makes for a
resonance called Fs. As soon as you put the driver in a cabinet you add
a second spring alongside the first - this is the springiness of the air
in the cabinet. The net effect is a stiffer overall spring which moves
the frequency of the resonance upwards.

Does that always shift the compliance limited range up to wavelengths
significantly shorter than the cone scale size? I assumed not.


I wouldn't have thought so.


But none of these things change the fundamental efficiency (sound power
out / electrical power in) of the speaker.

I am less sure of that. However I've never been though the details. nor
designed any speakers, so you may be correct for all I know. Interested to
see what responses you make to the above.


There is a standard equation that derives sensitivity (dB at 1 metre
for 1 watt)

112 + 10 * LOG(9.64 * 10^(-10) * Fs^3 * Vas/Qes)

I don't have the derivation for it, but if you check pretty much any
speaker manufacturer's data, the published sensitivity will match.

It occurs to me that horn loading will change this considerably, but
it really isn't equivalent because it sort of alters the assumptions
inherent in the T/S parameters by severely increasing the air mass
(equivalent density, if you like).

d