Subwoofer Measurement Tactics: Methods Continued Page 2
III. Ground Plane Measurement
We now come to an option that doesn’t require much more than a flat, solid, unobstructed surface such as an asphalt or concrete driveway or parking lot to rest the sub and measurement microphone on. Obviously, in being outdoors, you’ll once again be at the mercy of the elements as well as background noise pollution.
Don’t underestimate the latter’s measurement-corrupting capabilities: air or ground traffic or wind noise can easily mangle an otherwise good amplitude response measurement, as evident in the < 15 Hz portion of the blue and < 25 Hz portion of the red curves seen above . Depending on the nature of the background noise, redoing the measurements when all is quiet or averaging several measurements are effective antidotes.
Where the tower approach represents an attempt to eliminate boundary reflection by placing the sub well away from any reflective surfaces, ground plane measurement takes into account the effect of the single boundary the sub sits on. The acoustic signal reflected from the ground surface is considered to be a second, virtual source, identical to the actual source.
Based on the well proven, time tested method of images, ground plane measurement is an approach solidly grounded in science. To see why it works as well as it does, let’s look at the equation for the magnitude of the rms sound pressure, |p|:
(1)
Where:
|p| = magnitude of the rms sound pressure
A = magnitude of the rms sound pressure at unit distance from the center of each source
r = measurement distance
b = distance between the center of actual and virtual acoustic image
λ = wavelength of frequency under consideration
θ = angle to the perpendicular bisecting the actual and virtual acoustic images
Note that eq. 1 is for 2 acoustical sources, in this case the sub’s actual and virtual acoustic images.
At low frequencies (ie long wavelengths, where λ >> b), b is relatively small by comparison and the actual & virtual source will appear as a single source with sound pressure double that of the actual source alone. This doubling results in a 6dB increase of the measured axial sound pressure level above that produced by the same sub measured at the same distance under perfectly anechoic, free field conditions.
Care must be taken to ensure that measurements are, ideally, made with no large objects or reflective surfaces (other than the ground the sub sits on) within a radius ≥ λLF/2, where λLF equals the wavelength of the lowest frequency of interest. In this case a large “object” might be a barn or your neighbor’s house; a large reflective surface might be, for example, the side of a nearby apartment building or office tower.
Plot 2: Akabak Model: 12” Driver in totally enclosed box. Note interference effects from nearby boundaries.
Setting up for a ground plane measurement is pretty straightforward. Position the sub so its driver(s) are facing the measurement microphone; that is to say, lay the thing on its side. Then tilt the cabinet until the center axis, normal to the driver (or panel into which the drivers have been bolted, if 2 or more drivers are used) points to a spot on the ground 2 meters away. You may find using a laser pointer handy. Once the subwoofer has been oriented correctly, place the measurement microphone at the exact spot where the axis intersects the ground and measure away. But why measure at 2 meters when amplitude response measurements are typically made at 1 meter?
When the virtual & actual acoustic image outputs combine at the microphone, the net effect is to add 6dB to the axial sound pressure level. Doubling the measurement distance from 1 meter to 2 meters decreases the axial sound pressure level by 6 dB. As mentioned above, do so and the net result at the frequencies of interest produced by the subwoofer, is that the response will very nearly mirror that of the subwoofer measured free-field (or in an ideal anechoic chamber) only slightly altered by a few unavoidable acoustical artifacts.
Working up a model (15” driver in totally enclosed box) in LEAP 5 (plots at right), we see the reference free-air curve in blue, ground plane @ 1 m in purple and the ground plane curve scaled to 2m (red). As expected, the ground-plane at 2m is nearly identical to the free-air plot at 1m. Clearly, the ground-plane approach is an excellent, cost-effective (if not outright free) alternative if you don’t happen to have handy an anechoic chamber or a 100’ tower.
Given the ease of implementation, the data quality typically attainable and the minimal post-processing requirements, the ground-plane measurement technique (when done outdoors) is likely the best options available to the audio enthusiast.
