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Dr. Joseph D'Appolito,
Chief Engineer at Snell Acoustics, consultant for many manufacturers one of the most established speaker developer Author of e.g. Testing Loudspeakers, 1998 many DIY designs (no longer available) |

Interview to two driver in parallel,

Peter Strassacker asked Joe d'Appolito (7/2004).

Peter:

If I have a woofer with 90 dB SPL (2,83V/1m) and I add a second in parallel
(distance less than 1 wavelength), I measure 96 dB. So the input power doubles
but SPL goes up 6 dB what means an increase of factor 4 in power. Here an example
with two speakers of 10 inch; the diagramm shows the increase in dB.

**picture:**

measured

pressure gain of

two 10 '' drivers

with a distance

of about 15 ''

in parallel

compaired to one.

What happens?

Joe: The simple answer is that due to mutual coupling between closely spaced diaphrams, the effective radiation impedance is also doubled. Another way to say this is that the efficiency of the combined drivers has doubled and the total radiated power goes up by 4 or 6dB. This only occurs when the driver spacing much shorter than the wavelength of the sound they are producing and the drivers are essentially omnidirectional.

This increase in efficiency occurs only at low frequencies. At higher frequencies the situation becomes more complicated. If we consider the two drivers oriented vertically, then pressure will double at every point in the horizontal plane passing through the midpoint between the drivers. This is clear from the priciple of superposition. If each driver produces a pressure, P, then at any point on this plane the pressure from each driver will be in phase and will add to 2P or 6dB. However, above or below this plane the situation is quite different. Looking at a point above the plane, for example, the distance to that point from the upper driver will be shorter than the distance to that point from the lower driver. So there will be a phase difference between the two signals arriving at that point and the pressures will now add up to something less than 2P. In fact points will exist where the two arriving signals are completely out of phase and the pressure will be zero. The actual radiated power is now a complex function of frequency, driver spacing and driver polar response.

Peter:

Thank you Joe.