3 Attachment(s)
The quarter wave pipe: How low can you go ?
Quote:
Originally Posted by noah katz
Jack,
An amazing accomplishment.
One thing that puzzles me is how you can get such low extension from a TL of that length.
I calculate 1/2 wavelength corresponding to 4 m as 86 Hz, which I thought would mean LF starting to roll off at 43 Hz.
Thanks
Pipes (or any acoustic cavity with planar ends) that are closed at both ends exhibit their lowest resonance mode at a wavelength equal to ½ of the pipe length. (The same is true for room or box mode resonances). This is because both ends of a closed pipe (or a rectangular enclosure) have a positive reflection coefficient, (they act like an acoustic mirror), so half a wavelength looks exactly like an infinitely long wave, for F=1/2 L (and harmonics)
Pipes which are closed at one end, and open at the other end work differently. The closed end (with or without a loudspeaker) acts just like an acoustic mirror, as described above, however the reflection from the open end will see a negative reflection coefficient, caused by the abrupt drop in acoustic impedance at the open end. The reflected wave will have a 180° phase shift (polarity flip), the equivalent of an acoustic “anti-mirror”. This means that the lowest resonant frequency will now be F=1/4 Length of pipe (plus a slight end correction). Overtones will be at odd multiples of quarter wavelengths. (3/4, 1-3/4 …) An open ended pipe (transmission line) is tuned to ¼ of the pipe length, and is often described as a quarter wave (transmission) line speaker. In practice, the ¼ L 1st resonant mode, and harmonics will be shifted slightly upwards in frequency, depending on specific box construction.
In the case of my 18” Altec transmission line the tuning is as follows:
¼ * (334mps / 4m) = ~ 21.5 Hz.
The calculated quarter wave resonance may be suppressed or enhanced by the specific construction details of the transmission line cabinet, and TS parameters of the driver. In my case, I undersized the internal volume, and chose a diameter at the driver end which is very close to that of the speaker cone. Given the low QT and high Vas of the Altec 3182, this resulted in an over damped system (Q~ 0.5), with a LF roll off similar to that of an undersized closed box. In other words, the driver dominates the enclosure. The small internal volume also significantly reduces the port output at ¼ L, and higher (with stuffing). The Martin J. King TX simulation for my arrangement is shown below in the first figure in this post. The lower graph shows the cone output in red, and the port output in dashed-blue. The port contribution is minor compared to the cone output (not typical of transmission line speakers in general), resulting in a strong roll-off of the low frequencies. The device acts as a critically damped closed box of relatively small size, compared to the Vas of the driver.
The Martin J. King simulation indicates the requirement for approximately 12 dB/ octave low frequency compensation, but in practice, in my room, I have applied slightly less than 6 dB/octave, between 20-200 Hz in my system, so the question is: what mechanism(s) provide the additional required gain? (I use 15dB boost, while the simulation suggests >25dB is required at 20Hz)
As mentioned above, because of the small volume, my system is driver dominated, however this particular construction also generates a Helmholtz resonance at a frequency much lower than the ¼ L internal mode. The column of air behind the speaker cone acts as ported enclosure, with the air-slug mass working against the compliance of the driver. To my knowledge, only Martin J. King has reported this phenomenon in relation to transmission line loudspeakers. I first encountered the effect when I assembled my un-stuffed 4m line, and then pushed + released the Altec cone. The un-damped driver visibly oscillated with high amplitude for several seconds, at a few Hz. I was quite taken aback, never before having seen a driver do this without being connected to an amplifier!
Subsequent relative impedance graphs confirmed the lowest resonance frequency to be 4Hz in the 4m transmission line. (I used a CROWN DC300A for accurate response down to DC).
I also measured the transmission line relative impedance with only the internal tapered tube, equivalent to a 2m transmission line. The relative impedance plots for the un-stuffed and stuffed 2m and 4m lines are included at the bottom of this post. The 2m plots clearly show that the un-stuffed transmission line is behaving more like a ported enclosure, with the entire tapered tube acting as a very large & long port, to generate a very low tuning frequency (~8 Hz in the 2m tube). Note that the overtone distribution only vaguely adheres to simple quarter wave pipe theory due to the influence of the acoustic reactance associated with the ported enclosure (Helmholtz) response
The relative impedance graph for the 4m transmission line shows that the frequency has moved down to 4 Hz. In both cases, long hair wool damping reduces both the fundamental resonance, and overtones resulting in a smooth acoustic output from the cone. Although well damped, I note that the 4Hz resonance is still buried within this system, and so the port output at these frequencies probably augments the lowest frequencies below 10Hz.
Another contributor to low frequency reproduction in my system comes from “room gain”. Although many posts cite this effect as important for low frequency extension, in a typical room the effect is mainly one of near field proximity to acoustic boundaries, which limits radiation to ½ space, ¼, or 1/8th space, depending on distance from a corner. True room gain is common in small listening spaces, such as automotive interiors, where the cavity volume is so small that all bass waves are much larger than any of the internal dimensions. Domestic listening rooms are generally large, and commercial speakers have typical bandwidths which restrict LF or subsonic output such that true room gain is relatively rare.
Rare, yes, but not impossible, as explained in the following text, extracted from my website:
“Overall bass efficiency is likely due to the proximity of each driver to the three way corner (masonry walls and cement ceiling) such that over their entire bandwidth (below 110Hz) the Altec drivers are radiating into 1/8 space, i.e., the three rigid acoustic boundaries are within 1/8 of a wavelength for frequencies below 140Hz, which makes the apparent efficiency of the drivers about 9dB higher than if they were radiating into free space. (aprox 3dB for each boundary, ignoring absorbs ion and transmission losses.)
Furthermore, the dimensions of the room are such that for all frequencies lower than 35Hz, the shortest dimension, the 8ft ceiling height is less than 1/4 of a wavelength, and for all frequencies below 20Hz, the medium dimension of 14ft. will be less than 1/4 of a wavelength, and finally, for all frequencies lower than 15hz, even the longest dimension of 18.75 feet will be less than 1/4 of a wavelength. As the frequency drops below 35hz, each of the room boundaries will move through from the range of beyond 1/4 wavelength, down to less than 1/8 of a wavelength (at the frequencies of 17.5Hz, 10Hz, and 7Hz respectively). In other words, for frequencies below 140hz, the ceiling is within 1/8th of a wavelength, and augments the sound pressure level by almost 3dB, when the frequencies go below 35Hz, the floor is also close enough to start contributing to the SPL of the sound, and this increases as the frequency is lowered to 17.5Hz, where the floor is 1/8th of a wavelength from the driver, and the phase of the waveform is nearly identical, regardless of height, and the SPL will get almost a 3dB boost below 17Hz. Likewise, for frequencies below 20Hz, the side walls start adding in phase, reaching maximum contribution below 10hz (another 3dB), and the longest dimension contributes below 15Hz, ramping to 7.5Hz at which point the room will be in complete isophase condition.
Of course wave fronts still propagate throughout the room at the speed of sound for these low frequencies, however the rate of change of pressure amplitude will be so slow, and the wavelengths so large, that each point in the room will appear to have identical pressure amplitude, and phase for these low frequency waveforms. At frequencies below 7Hz, essentially all six of the room boundaries will be closer than 1/8th of a wavelength, and this will yield an extra 9dB of gain, for a grand total of 18dB extra SPL when the corner placement is included. The natural progression across the 1/4 to 1/8 wavelength (zero dB to +3dB increase) combined with the staggered dimensions deliver a gradual ramping up of room gain, which mimics the missing boost below 20hz. The trick is particularly effective in the current room, because of the full masonry construction of the four walls, and the uncommon use of prefabricated concrete floor and ceiling, such that the low frequency reflection coefficient is very near unity. “
Jack Bouska
5 Attachment(s)
Construction of the "Impact Stack" post 1 of 2
Quote:
Originally Posted by
Flodstroem
I have read all your posts with great interest and everything you write ("say") seems to be so obvious to me that I think I must try some of your ideas and suggestions.
Thanks for the feedback, I hope my comments on system philosophy and horn design will be of some use to you in your speaker building projects.
Also, apologies to the Lansing heritage membership for my recent inactivity. For the last three months, it seems my spare time is measured in negative numbers! I seem to be inordinately busy at work, with my evening and weekend free time consumed by preparation for some unexpected external commitments to the European Association of Geoscientists and Engineers (see:
http://www.eage.org/index.php?Menu_Code=DLPCourseDetails&EVS_Id=197&Ac tiveMenu=85&Opendivs=s19,s36
and
http://www.eage.org/index.php?Menu_Code=SCPCourseDetails&EVS_Id=191&Ac tiveMenu=85&Opendivs=s19,s41
Quote:
Originally Posted by
Flodstroem
When reading all your posts I couldn't find any information regarding how you built those round "hat-boxes" for your speakers (for the 1401ND, and the 2123H). I am aware of that, they was made out of two boxes, one in another, with air in between them for to not get acoustic resonances from standing waves from the inside to the outside. But how did you built them?
A picture is worth a thousand words, so rather than write another series of long posts (which I still cant afford the time for), I am including a series of photo's taken during the construction of the speakers. (in this, and a subsequent post.)
The pictures are numbered and captioned, and should be mostly self explanatory. If you have specific questions, or want more info related to some aspect of the process, you can post your question with the photo number as reference, and I can comment appropriately.
Jack
5 Attachment(s)
Construction of the "Impact Stack" post 2 of 2
Post number two (of two)
The pictures are numbered and captioned, and should be mostly self explanatory. If you have specific questions, or want more info related to some aspect of the process, you can post your question with the photo number as reference, and I can comment appropriately.