Speaker spatial loading is determined by the boundaries which are in close vicinity of the object that radiates sound. This will determine a certain load. Similar to the load on an amplifier, which will give more power to a lower impedance speaker. Something similar happens with the acoustical load. The acoustical load is defined by the space which the sound radiates in, which is measured in steradians. Stick with me, it will make sense soon.

I’m not going to go in full details about the steradian, you can read more about it on wikipedia. I will, however, try to be as brief as possible, so you can get somewhat of an idea.

You got these 2 types of units of measurement :

What is a radian? Picture the radius of a circle. Following the circumference of the circle, draw an arc with the exact length of the radius. That’s 1 radian. The whole circumference of the circle will measure around 6.3 radians. The exact number is 2π radians.

What is a steradian ? Picture a sphere with the radius r. Now imagine a circular patch on this sphere, which has the area equal to r2. That is 1 steradian. Anyway, what is important to know is that the whole sphere has a total surface area of 4π steradians.

The sound, when produced, it radiates in all directions, much like a sphere. Imagine a sphere that is growing and growing. That is how sound radiates, if no obstructions are met. A perfect sphere.

Depending on the space in which the sound is radiated in, the speaker spatial loading is of several types :

#### Full space – 4π steradians

This is the exact same thing like the sphere I was talking about, and that is the reason why it’s 4π steradians. The sound is travelling normally into all directions with no boundaries.

#### Half space – 2π steradians

This is a typical example of infinite baffle. Imagine a speaker placed on a baffle that extends indefinitely in all directions. To make it more realistic, the baffle should be wide as the wavelength of the lowest frequency produced by the speaker placed on the baffle. Pretty wide if it’s a woofer. Because of this, the sound cannot expand in the spherical fashion. The baffle is in its way. For this reason, the other half of the sphere, which should of gone backwards, is going forwards. You can imagine 2 half overlapped spheres expanding in the front of the baffle. This will create and additional boost in output of +6 dB.

#### Quarter space – π steradians

Imagine that you place the speaker at the intersection of two infinitely large perpendicular planes. Something similar in real life would be the corner of two walls (the floor + another wall). Doing something like this will cut the sphere into 4, and the sound is forced into a quarter of a sphere. The additional sound boost is of +12 dB in this case.

#### Eighth space – π/2 steradians

Imagine that you position the speaker at the intersection of three infinitely large perpendicular planes. Something similar in real life would be the corner of a room. This will reduce the size of the sphere to 1/8, and the sound is forced into that small space. The additional sound boost is of +18 dB for eighth space.

You can go even lower than eighth space, by using horns. The acoustic radiation of the speaker is funnel into such a small solid angle, and as a result. the boost in sound is of great proportions. For this reason, horns are often a great solution to improve the efficiency of a driver. I remember I used to do this in school, without knowing exactly how it work : when I listened to music on my phone at maximum volume, but wanted to increase it, I would make a small opening in my fist and place it over the speaker. I can tell you right now, it was a pretty bad horn design, but the increase in output was noticeable.

### Baffle step

A particular example of half space loading is on a normal loudspeaker enclosure. Usually, the enclosure will be a rectangular shaped box with a front baffle, where the speakers are mounted. Since you position the speakers on a baffle, this creates a half space environment The baffle forces the sound to go only in the front, and not to the back. However, this does not happen equally to all frequencies. It depends on the size of the baffle. Every frequency has its own wavelength which is a unit of distance (length). If you take the wavelength of a particular frequency, and if it’s larger than twice the length of the baffle, then that particular wave will radiate into full space. The baffle is not large enough to force that particular wave forwards (half space), therefore that wave will expand into all directions, including the back of the baffle.

### How to design loudspeakers - video courses

High frequencies have small wavelengths and low frequencies have large wavelengths. Depending on the size of the baffle there will a point, when you go lower and lower in frequency, where the waves will stop radiating into half space and transition to full space. For this reason, on a typical loudspeaker enclosure, high frequencies and some midrange frequencies will get a +6 dB boost by the baffle, and low midrange plus low frequencies will not. When you are designing a loudspeaker system, take into consideration this particular speaker spatial loading. The difference of +6 dB is considerable and affects linearity by a great deal. This is usually taken care of in the crossover section of the system, by attenuating the high frequencies.

### Conclusion

Speaker spatial loading is very important when designing an audio system as a whole. We talked about the baffle step which affects some of the audio bandwidth, but also the room where the loudspeakers are place has a significant impact on the frequency response of the system. The low-end spectrum will get a significant boost, depending on the size of the room . This is called the room gain. Some people prefer to place their subwoofer in the corner of the room. As a result, they get a large boost on the low notes, since the subwoofer is radiating into eighth space. If you are knowledgeable in speaker spatial loading, you can use it to your advantage and make clever use of “free environment”. However, sometimes it doesn’t work in your favor and you have to compensate for it, to meet your expectations.

#### References

1. Introduction to Loudspeaker Design: Second Edition by John L. Murphy (True Audio, 2014). (Amazon affiliate paid link)