Reliable frequency range for ground plane measurements

[JMB]

There appears to be a discrpancy in the upper reliability reported in two sources.

I read in D'Appolito that the reliable upper frequency is:
for 1 dB error: 25.7*10^4/(l*m)
for 3 dB error: =42.9*10^4/(l*m)

where:
l = Distance from ground to the of center of the driver (cm)
m = Height of microphone (cm)

I also see on the Audioholics sight the formula:
IpI=2*A/r*sin((2*pi*b/l)*sin θ)/(2*sin(pi*b/l)*sin θ)
where:
|p| = magnitude of the rms sound pressureA = magnitude of the rms sound pressure at unit distance from the center of each sourcer = measurement distanceb = distance between the center of actual and virtual acoustic imagel = wavelength of frequency under considerationθ = angle to the perpendicular bisecting the actual and virtual acoustic images

I realize that the latter formula is calculating sound pressure from two non completely correlated sources but in calculating at different frequencies, I start to see a significant error by a few hundred hertz whereby D'Appolito's formula suggests that with a small enough baffle on the ground and enough reflection free clearance, you could get full range measurements. For example, for a 1 dB error with a 40 cm baffle and the mic center 0.5 cm above the ground, you get measurements to 25,700 Hz. I would love some insights and guidance from anyone.

Thanks,
__________________
Jay

[weltersys]

Originally Posted by JMB

There appears to be a discrpancy in the upper reliability reported in two sources.

I realize that the latter formula is calculating sound pressure from two non completely correlated sources but in calculating at different frequencies, I start to see a significant error by a few hundred hertz whereby D'Appolito's formula suggests that with a small enough baffle on the ground and enough reflection free clearance, you could get full range measurements. For example, for a 1 dB error with a 40 cm baffle and the mic center 0.5 cm above the ground, you get measurements to 25,700 Hz. I would love some insights and guidance from anyone.

Thanks,
__________________
Jay

Jay,
Different measurement conditions will result in different results at different frequencies, not a broad band difference.

Reflections off the ground can cause path length differences at the mic, resulting in peaks and dips.

Your questions made me compare some measurements I on a top cabinet which normally would be off the ground with the center of the two 10 inch speakers up about 73 inch high. Measurements were with the mic 60 inches from the front of cabinet.

With the speaker and mic in air, the cabinet rolls off at about 93 Hz.
On the speaker and mic ground, the roll off starts about 75 Hz, but "bumps" at 140 and 170 Hz appear.

The speaker is 33.75 tall, 13.5 wide, speaker center is 16 inch from the bottom, ports on the bottom. Horizontal and vertical tests were done on the ground, both with the speaker baffle angled towards the mic. The horizontal position looks quite similar to about 315 Hz, but above looks different from both the vertical measurements.

The orange measurement is interesting in that the midpoint of the speaker is at 73 inch high, but the mic is on the ground, still 60 inch from front of cabinet, but the path length to the mic is longer, and the speakers way off axis. The LF roll off is now about the same as when the speaker is on the ground, even though it still is in the air.

Art Welter

[JMB]

Hi Art,
Thanks for responding.

Did you average your measurements; if not, it is possible that environmental noise may have impacted them accounting for the differences at higher frequencies. Also, the change in baffle direction may have impacted them as the baffle step signature would change; the edge against the ground is essentially doubled due to the mirroring effect.

I ran your numbers through the two formulae above:

D'Appolito would suggest your good to 1 dB till around 12.7K while you would be good to 3dB error to 21.1K. Audioholics would suggest about 5.1K and 9K, respectively. I lean towards the latter.

I am not surprised at the lack of low frequency impact from being off of the ground. I think that if the mic is on the ground, it can't really pick up many reflections except from surrounding structures, but this would be the same whether the speaker is on the ground or in the air. You would lose S/N with increased distance.

Jay

[weltersys]

Originally Posted by JMB

Hi Art,
Thanks for responding.

Did you average your measurements; if not, it is possible that environmental noise may have impacted them accounting for the differences at higher frequencies. Also, the change in baffle direction may have impacted them as the baffle step signature would change; the edge against the ground is essentially doubled due to the mirroring effect.

I ran your numbers through the two formulae above:

D'Appolito would suggest your good to 1 dB till around 12.7K while you would be good to 3dB error to 21.1K. Audioholics would suggest about 5.1K and 9K, respectively. I lean towards the latter.

I am not surprised at the lack of low frequency impact from being off of the ground. I think that if the mic is on the ground, it can't really pick up many reflections except from surrounding structures, but this would be the same whether the speaker is on the ground or in the air. You would lose S/N with increased distance.

Jay

Over the frequency range tested, the coherency was quite good, and averaging was over 1360 ms. The differences you see in the graphs are real and repeatable, not environmental noise.
Over half my time testing outdoors is waiting for a point between wind gusts to get decent traces. Above about 3K, the waiting gets longer...

The "baffle step signature" the transition between 250 and 125 Hz did not change from horizontal to vertical.