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Accuracy Applied: Part 1 In A Series On The Keys Of Loudspeaker Measurements

"Frequency response is the single most important aspect of the performance of any audio device. If it is wrong, nothing else matters." – Floyd Toole, 2009

Sound Fields

When conducting loudspeaker measurements, the concept of sound fields is important. Acoustic loudspeaker measurements should be conducted in a free field, which is a region in space around a sound source where sound may propagate freely in all directions with no obstructions.

An idealized example of this is a point source (an object that is small compared to the wavelength of sound radiating from it) located high above the ground and away from any reflective surfaces. When an idealized point source radiates sound in a free field, the sound intensity (sound power per unit area) is inversely proportional to the square of the distance from the source Figure 1.

Figure 1: An idealized point source radiating sound in a free field.

Sound intensity is proportional to sound pressure squared. Hence the sound pressure level decreases by 6 dB per doubling of the distance from the source. This phenomenon is sometime called the inverse square law or 6 dB/dd rule.

If a loudspeaker and microphone are in a free field, the mic will measure only the direct sound radiated from the loudspeaker. This is desirable – we want to measure the sound radiated from the loudspeaker itself, to have data that is representative of the loudspeaker, independent of the environment in which it is located.

If instead, the loudspeaker and microphone are located in an ordinary room, in addition to measuring the direct sound, the microphone will measure sound reflected from the floors, walls, ceiling and any large objects within the room (Figure 2). The direct sound will arrive first at the mic, followed by the first reflections from the closest surfaces and then secondary and tertiary reflections.

Figure 2: A loudspeaker measurement in an ordinary room.

Relative to the direct sound, the reflected sound waves will be lower in level depending on the absorptive properties of the surfaces they reflect from and the path length difference. The path length differences also cause delays between the arrival of the direct sound and the reflections. These reflected sound waves contaminate the direct sound, causing an incorrect estimate of the sound radiated from the DUT and its frequency response.

An ordinary room is considered to be a semi-reverberant sound field, because surfaces in the room absorb a portion of the sound waves incident on them. The degree of absorption depends on the surface finish (for example, carpeted floor versus concrete floor) and it also varies with frequency. A fully reverberant or diffuse sound field can exist in a special room called a reverberation chamber which has walls, floor and ceiling constructed from hard surfaces designed for maximum reflections. In a diffuse sound field, sound waves are traveling randomly in all directions with equal probability.

In some cases, when testing a loudspeaker drive unit alone, measurement standards specify a half-space free field. As the name implies, in a half-space free field, the 3-dimensional space that a sound source is free to radiate into is split in half, usually by a hard, reflecting plane.

One example of a half-space free field is a sound source located outdoors on hard ground, far away from any other reflective surfaces. Another example is a hemi-anechoic chamber, in which all the room surfaces are highly absorptive except the floor, which is made of a hard, reflective material like concrete. A free field and half-space free field are sometimes referred to as a 4π (4 pi) space and a 2π (2 pi) space, respectively. This is based on the solid angle in steradians that a sound source can radiate into without obstruction.

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Another important concept in acoustics is the near field and far field. Far away from a source (relative to its size), the inverse square law (or 6 dB/dd rule) mentioned above applies. At this distance the sound field has become stable and radiates from the source in a predictable way.

Close to the source, however, sound waves behave in a much more complex fashion and there is no fixed relationship between pressure and distance. In this near field, the sound level is uncertain.

Therefore, measurements should be conducted in the far field. The distance from the source to the far field depends on the size of the source. As a “rule of thumb” it is typically considered to begin at a distance of three times the largest dimension of the source [5]. However, it’s been suggested that the far field begins at three to 10 times the largest dimension of the source [6].

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