Re: Speaker sensitivity and fs in multiples.

[EMAIL PROTECTED] (Bob-Stanton) wrote in message news:<[EMAIL PROTECTED]>...
> [EMAIL PROTECTED] (Svante) wrote in message 
> 
> > 
> > You cannot sum the powers. You have to sum the sound pressures. The
> > sum of four 1/2 pressures is 2. So, sound pressure will double (+6.02
> > dB) for the same input power.
> > ...
> > 
> > No, again you cannot sum the individual powers. 
> 
> To say: "You cannot sum individual powers", is a violation of the law
> of conservation of energy.

Assuming that there is no change in the acoustic power from each
speaker... You are going in circles, you say that efficiency does not
change, because efficiency does not change.

> Another fundamental law a physics is Energy = Force * Distance. If
> each of four drivers in an array is pushing the air with half the
> force, for half the distance, each puts out 1/4 the energy.  The total
> power output of four will be only the same as a single driver.

The distance is halved, but the force is not. Each driver sees the
pressure created by itself, but also the pressure from three more
drivers. Thus the pressure is four times half the original pressure (=
two times the original pressure), and thus the force is doubled. So if
energy = force * distance, and the force is doubled, the distance is
halved, and the number of drivers is four, the net energy will be four
times the single driver.

> > For the system, total
> > displacement will be x*2. This is acheived with the the same input
> > power. This corresponds to an increased efficiency of +6.02 dB.
> > 
> 
> Thats right.   BUT
> the force exerted by the drivers in the array is only 1/2 that of a
> single driver, that corresponds to a decreased efficiency: -6.02 dB.

Nope, see above.

> 
> 6.02 dB -6.02 dB = 0 dB change.
> 
> P = F/2 * x*2 is the same pressure as: F * x.  That means NO increase
> in pressure, No incease in effiency and no increase in power.
> 
> 
> > > > This reasoning holds for low frequencies, ie when the drivers are
> > > > mounted close to each other compared to the wavelength. For higher
> > > > frequencies it holds straight in front of the speaker (anechoic
> > > > conditions) but to the sides, interference will decrease the sound
> > > > pressure. So for higher frequencies, on average (over frequencies and
> > > > directions) your statement ends up correct (ie the
> > > > efficiency/sensitivity is the same)
> 
> 
> > No. Given an ideal piston driven to an acceleration corresponding to
> > the signal, the level EXACTLY straight in front of and far away from
> > the piston does NOT vary with frequency. To the sides it does. To the
> > sides the level will vary towards higher frequencies due to
> > interference from the different parts of the piston. This will cause
> > on-axis level to be constant (vs frequency), but efficiency to drop
> > towards higher frequencies. Thus, the efficiency gain I have described
> > in this thread is only acheived in the low-frequency region.
> 
> At higher frequencies, as the polar pattern narrows, the energy will
> be concentrated toward the front. The sound pressure level will
> increase.
> 
> Bob Stanton