So I am designing a speaker where the woofers are dual opposed in a front to back fashion, crossed at 400Hz. The enclosure is 7.5" deep. Physics tells me that I should have a dip around 500Hz due to the 7.5" distance between the front and back woofer and the cancellation caused by the rear woofer being delayed compared to the front woofer. Boxsim shows that there is a dip starting at just 200Hz with the trough at around 500Hz.
However, we also know that if two sound sources are within 1/4" wavelength apart, the two sources couple and act as one source with the acoustical center between the center of the 2 sources. 1/4" wavelength of 7.5" is equivalent to 450Hz. This should mean below 450Hz the 2 woofers should couple as one with no dips.
Which one is correct?
However, we also know that if two sound sources are within 1/4" wavelength apart, the two sources couple and act as one source with the acoustical center between the center of the 2 sources. 1/4" wavelength of 7.5" is equivalent to 450Hz. This should mean below 450Hz the 2 woofers should couple as one with no dips.
Which one is correct?
I think Boxsim is correct about the dip. I think also that you read too much into the 1/4 wavelength separation rule. If the two drivers were on the same baffle facing the listener, then the acoustic center would indeed be between them but when one is on the back of the box and has a different path length to the listener, you should expect consequences from that difference in path length.
The actual (acoustical) spacing between the woofers is larger than the depth of the cabinet, as it also has a width. The sound first has to go around the cabinet, it cannot pass right through it. Think of flat baffled dipoles: even with a depth of only the wood thickness (almost zero), they still work fine.
The 1/4 wavelength rule is more a rule of thumb: there is a more or less gradual transition from full coupling (zero distance) to no coupling at all (large distance). So even at 1/4 wavelength spacing, there is no full coupling.
The 1/4 wavelength rule is more a rule of thumb: there is a more or less gradual transition from full coupling (zero distance) to no coupling at all (large distance). So even at 1/4 wavelength spacing, there is no full coupling.
I'm thinking Boxsim is wrong. If Boxsim is correct, then dual opposed subwoofers would start dipping near 100Hz and have a full dip at around 150Hz. Looking at outdoor ground plane measurements of several dual opposed subwoofers, I see no such dip.
Do you know where the mic was positioned for those outdoor measurements, in line with the two drivers or equidistant from both? Or where Boxsim assumed it to be?
The rule of thumb for 1/4 wavelength is with respect to offset between acoustic centers, not with respect to path length difference.
1) You can have 2 drivers with 0 path length difference to the mic (or listener), but spaced an infinite number of wavelengths apart.
2) Conversely, you can have two drivers spaced less than 1/4 wavelength apart, but have an extreme path length difference (in terms of relative proportion).
For example 1), simply consider a stereo pair of speakers arranged such that the speakers and the mic form an equilateral triangle of side length 1 kilometer.
For example 2), consider two woofers (flat-diaphragm for argument's sake) adjacent to each other on a flat baffle, but with the mic spaced so it is almost touching the center of one of the woofers.
1) You can have 2 drivers with 0 path length difference to the mic (or listener), but spaced an infinite number of wavelengths apart.
2) Conversely, you can have two drivers spaced less than 1/4 wavelength apart, but have an extreme path length difference (in terms of relative proportion).
For example 1), simply consider a stereo pair of speakers arranged such that the speakers and the mic form an equilateral triangle of side length 1 kilometer.
For example 2), consider two woofers (flat-diaphragm for argument's sake) adjacent to each other on a flat baffle, but with the mic spaced so it is almost touching the center of one of the woofers.
Unfortunately I don't know for sure. I believe he measures it with one woofer facing the mic. I do know he applies a correction to the measurements because he investigated and concluded that a dual opposed subwoofer needs the correction, otherwise the output is understated because the output from the other driver isn't coupled properly to the front woofer.
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