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Topic No. 1

Loudspeaker Spatial Loading
John L. Murphy
Physicist/Audio Engineer


 The frequency response of a loudspeaker system depends on how the system is "loaded" in much the same way that the output from a power amp depends on the load impedance. The power amp drives an electrical load specified in Ohms. The speaker drives an acoustic load specified in "solid angle" or steradians. The most commonly specified speaker load, and the one typically specified in the loudspeaker literature, is half space.

Here are the commonly specified acoustic loads:

Full Space = 4 pi steradians
This represents radiation into free space, that is in the open with no walls, floor or surfaces nearby.

Half Space = 2 pi steradians (commonly specified speaker load)
If you imagine putting a speaker on an infinitely large baffle then the front of the speaker would be radiating into half space. The plane divides all of space into two halves.

Quarter Space = pi steradians
Imagine the speaker placed at the intersection of two infinitely large perpendicular planes. Approximated by the intersection of two walls. The two planes divide all of space into four quarters.

Eighth Space = pi/2 steradians
Now, imagine the speaker placed at the intersection of three walls, such as in the corner of a room and at the ceiling. The three planes divide all of space into eight parts.

Smaller Acoustic Load Angles
In horn type loudspeakers the acoustic radiation from the horn driver is funneled into an even smaller solid angle than "eighth space" and achieves increased power output as a result of the horn load. The smaller solid angles constitute a "stiffer" acoustic load and draws more power from the source analogous to the way that a lower impedance speaker draws more power from the amplifier driving it. Indeed, horns have been likened to "acoustic transformers" for the way that they can be used to match the impedance of the driving source to the impedance of the load to effect maximum power transfer.

The notion of the acoustic load that a speaker is driving is very important to understanding the reproduction of sound and especially important if you are trying to understand the net output of a speaker into a listening room.

 Speakers rarely see a constant acoustic load. It is almost always frequency dependent. Here is a sketch of how it plays out in a typical listening room. Regardless of how it is placed in the room, a typical hi-fi speaker system sees a half space load at frequencies from the midrange up as a result of the drivers being placed on the flat baffle (front face) of the box. At high frequenciess the drivers only radiate to the front of the box. Starting in the midrange (depending on the baffle size) the system shifts from radiation into half space to radiation in full space at lower frequencies. Another way to say this is that the bass radiates in all directions . . .even to the back. This transition from half space loading to full space loading results in what is commonly called the "6 dB baffle step", or "diffraction loss", and results in a 6 dB loss of bass with respect to the midrange output. At even lower frequencies, say from 100 Hz down, the wavelength of the radiated sound is such that the walls and cavity of the listening room begin to load the system in a way that results in a complex load that is less than half space and results in increased output from the system. This effect in the bass is called variously "room gain", "boundary effects", "room resonance", "frequency dependent radiation impedance", etc.


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