Next measurements were performed to gain more insight in the magnitude bump around 400 Hz as "discovered" by John. I was able to recreate those under similar circumstances such as distance and baffle width but, going through older measurements, I found that there were many instances where this bump was not visible. I found also similar bumps centered around other frequencies with different baffle widths. Question coming up was: is this a baffle induced effect (diffraction ?) or is this a "floor-mirror", "floor-bounce" ... ? Or is this a compound effect, a little bit of everything ?
I attached a 25" wide baffle with a mounted RD75 on a balcony overlooking my listening space where I usually perform the measurements. The bottom of the driver was sitting 10.5 feet above floor level. Microphone was rigged 80"'s (+/- 2 meter) from the ribbon at a height of 13.75 feet. This is a similar set-up as I would normally use on floor level, this time 10.5 feet up in the air.
The first figure below shows 4 measurements performed under slightly different software settings/instrumentation settings. Goal was to rule out measurement variations since John and I are both working with different preferences based upon the available equipment.
The first measurement (red plot) was performed using a in room SINE (not gated) instrument. This yields good resolution in the low end because of the logarithmic spaced frequency intervals. (200 in this case) This non gated type of measurement however is sensitive to the inevitable standing waves in the room, hence some more dipping and peaking as compared to an MLS measurement which doesn't create as much standing waves since it doesn't excite the room with sine wave bursts.
The second measurement (white plot) was taken using a 16 k sample MLS instrument with a 4096 FFT, my usual set-up. This results in a 85.3 ms time interval that is analysed. Practical: a big chunk of the room response is included, similar as the measurement performed with the SINE instrument. Taking the differences into account, the correlation between the red and white plot is acceptable in the region of interest: 100 - 1 kHz.
The yellow plot is taken from the same impulse response as the white plot. The major room echoes have been gated out until a measurement interval was left of 19.5 ms. Good for a frequency response down to almost 52 Hz. Since the FFT analysis contains less data, the frequency bins will be larger, resulting in some resolution loss. Since 3/4 of the room response has been cut away, expect also a drop in average loudness level. Both effects can be seen by comparing the white and yellow plot.
The brown plot was again taken from the same impulse response, this time with a 512 FFT window. The impulse response is "windowed" with a Bingham window, a similar setup as used by John Whittaker. Correlation between the yellow and brown plot is good. The shift in the magnitude bump can probably be attributed to the FFT resolution difference and the use of a different windowing function.
The nice thing to notice is that the MLS curves are relatively flat, +/- 3 dB from 600 Hz to 16 kHz for inroom response, the response with echoes removed is even better, +/- 2 dB in the same frequency band.
The observation to make however is that the infamous bump is present, even if there is no floor. The magnitude of the peak (8-9 dB) is at this distance (2 meter) is the same as measurements performed at floor level. Which brings up the question: is this a baffle induced effect ? Measurements at floor level show the peak dropping down to 6 dB at 3 meter, 2-3 dB at 4 meter and virtually gone at 5 meter. (Dipole quarter wave cancellation showing up again for those frequencies that are not supported by the width of the baffle.)
The plot below shows response taken in the same position with the microphone lowered down. Interesting to see is the large difference when going below "floor level" Measured response time in these plots was 85.3 milliseconds.
What's next ? A repeat of this test in a much larger environment allowing fully pseudo-anechoic measurements in an effort to exclude most of the environment interaction.
Thanks to Doug Stabler, for removing my mental block with respect to the possibility of dipole reinforcement, and thanks to John Whittaker for insisting during subsequent telephone conversations that I did have literature about the concept. (Development of a Compact Dipole Loudspeaker by Siegfried Linkwitz.)
The above graphs show that the "bump" was not really a single peak but a collection of peaks and nulls. (Visible in the higher resolution plots.) Since the above plots show a lot of room response and lack resolution in the region of interest (< 2k), I whipped a large baffle up on a Carver ribbon, suspended it from the balcony and measured this combination with a gated SINE instrument. This allows for pseudo anechoic measurement with high resolution in the lows. This plot is shown below without any curve smoothing, so peaks and dips are deep ! BSP goes a long way in making sure we don't hear them the same way as we see them ;-)
The "bump" of interest is not a single peak, it is rather 3 peaks and 2-3 dips. Definitely proof that the complex is made up out of phase cancellation and reinforcement. Notice also that some of the peaks and nulls have an harmonic relationship as one would expect in this case..
Linkwitz models in his article an idealized dipole as a positive and a negative acoustic point source, spaced at a distance (D) from each other. The response is sloping at 6dB per octave below the frequency of the first peak. (Can be seen in some of the frequency/magnitude graphs on non baffled drivers.) The on-axis peak occurs where D equals half wavelength or at a frequency Fpeak = 340 m/s /(2*D). Linkwitz writes further: "The rear radiation is in phase at this frequency with the front radiation and the output is doubled (+ 6dB)" The peak is followed by nulls at even multiples of Fpeak and further peaks at odd multiples of Fpeak.
This is valid for a single point source on a circular baffle. I assume that a linesource with rectangular baffle will need a slightly different model, the main idea remaining the same. (BTW, the top red and white plot of the BG's on a 25" baffle show the first peak correlating with above formula.)
I also observed the "bump" changing shape and magnitude with varying measurement distances, indicating that the dipole reinforcement is not the only mechanism at work. I've seen this so far only on baffled drivers, raw drivers roughly following the 6dB/octave drop. At close range from the driver the bump reaches peaks of 9-10 dB, ample indication that there is more than one reinforcement mechanism at work
Hence following thought: the rear wave and front wave of a baffled driver reach the ear via different path lengths in an on-axis situation. The frontwave reaches the ear directly, the out-of-phase rearwave travels half the baffle width + a diagonal path to the ear. The difference in travel distance and the out-of-phase character of front and rear wave will yield a cancellation/reinforcement signature at the listener's position. It is obvious that at large listening distances the difference is governed by half the baffle width. That's probably the reason why at larger distances the bump flattens out. Some dips and peaks overlap/cancel since they are roughly based on D (baffle) and D/2 (half the baffle width)
Conclusion: it seems that there is handle on the problem. There is at least need for two models, one for a line source with rectangular baffle, and a similar model that plots frequency/magnitude in function of baffle width and listening distance. The combination of both and verification with real-life measurements will show if there needs to be a search for the next mechanism ;-)
To be continued.
Time to get MathLab out of the box. ;-)