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Bass From Small Woofer Vs Big Woofer

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  • Bass From Small Woofer Vs Big Woofer

    Hi guys, another noob question, but I hope an interesting one...

    ScanSpeak do a nice looking 32cm woofer ( that they say models down to 34Hz in a 69l vented enclosure. They also do a very nice looking 18cm woofer ( that models down to 34Hz in a 39l enclosure.

    There are some obvious differences here in size of the enclosure and sensitivity, but my question is: What are the audible advantages of one over the other?

    Looking at the SPL graph, it looks like one has a smoother curve at the lower ranges. I guess that means it'll sound nicer, or will that flatten out once it's in the cabinet?

    As usual, your knowledge and experience are always appreciated.

    Thanks in advance

  • #2
    One obvious difference is the small cone has to move further to make the same amount of bass. At very low volumes, and only reproducing a single frequency, that's not a big deal if the driver is designed for that. I mention single frequency, because a cone moving long distances to reproduce bass will modulate higher frequencies. Here's a primer:

    Rod is certainly not the first one to note the effect. Various designers as far back as the 40s wrote papers about it. These days when woofer cones can reliably move long distances, it becomes even more of an issue.

    To the ear, the effect is intermodulation, just like the more "conventional" IM associated with harmonic distortion.

    One way to minimize the effect in any event is to offload deep bass to a sub or subs.


  • #3
    Every diaphragm size has an ideal frequency range its just physics.

    1-2inch tweeter

    3-4inch midrange

    5-8inch mid bass/mid woofer

    10inch and up bass/sub bass/woofer.


    • #4
      Re: small woofer versus big woofer

      In an ideal model of a pistonic woofer in infinite baffle alignment radiating into free field half-space, 2pi spherical, operating at frequencies where wavelength is large relative to diaphragm geometry, there is an inverse square relationship between frequency and swept volume at constant SPL (flat frequency response), requiring quadrupled swept volume at halved frequency (one octave).

      Restated a little differently, the excursion limited response (likewise of a pistonic woofer in infinite baffle alignment radiating into free field half-space) exhibits constant -12_dB per octave slope with respect to decreasing frequency.

      That is why larger and/or more woofers are used to make SPL at lower frequencies.
      "Our Nation’s interests are best served by fostering a peaceful global system comprised
      of interdependent networks of trade, finance, information, law, people and governance."
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      (a lofty notion since removed in the March 2015 revision)


      • billfitzmaurice
        billfitzmaurice commented
        Editing a comment
        Larger or more, but since using more smaller drivers tends to be more expensive than one larger driver the larger driver option usually wins out.

    • #5
      Thanks all, great answers. I read each post and comment a couple of times to understand and appreciate them.

      hypothetically: I wonder if you made a massive array of tweeter (to create an over all very large surface area), so that those drivers were hardly moving at all, if that would be ok to play high and low frequencies because the lack of movement would mean little opportunity to distort? My gut tells me that there would be other problems resulting from the design, other than just cost and space.


      • LewisH
        LewisH commented
        Editing a comment
        I was thinking of the array to reduce distortion across the full range, rather than anything else

      • billfitzmaurice
        billfitzmaurice commented
        Editing a comment
        An array does reduce distortion, but it still won't make a tweeter into a woofer.

      • LewisH
        LewisH commented
        Editing a comment
        Why wont it reduce distortion? Surely it will mean a greater Sd and therefore less cone movement, therefore less distortion?

    • #6
      EXCURSION: The "effective piston area Sd" of the smaller one is 154 sqcm. The larger one is 526 sqcm. This means that when they are both moving 1mm, the larger one is displacing 3.4 times as much volume as the smaller one, meaning it is playing about 5dB louder, or a note that is almost an octave lower. When they are both playing the same note at the same SPL, the smaller one is moving 3.4 times farther than the larger one. The "Linear excursion" (Xmax) measurement is about the same (7mm and 9mm), so the smaller one will exceed that limit at much lower volume, or higher frequency, than the bigger one. When the smaller one is moving 7mm, the larger one will be moving only 2mm.

      In general, the farther a cone moves, the more it distorts. Plus, there is the intermodulation distortion mentioned by fpitas, which gets worse the farther the cone is moving.

      If you want the same SPL from the smaller one with the same excursion at a given frequency, you would need 3.4 of them (which is to say 4 of them) to replace one larger one.

      One advantage of using multiple small woofers, besides the aesthetics and practicality and diffraction advantages of a narrower cabinet, is that you can arrange them for WMTMW (or WWMTMWW), or you can arrange them to control the vertical reflections from floor and ceiling.

      The "Max mechanical excursion" (Xlim) on the larger one is twice that of the smaller one, which means that once they pass the Xmax "limit" the larger driver will go 6dB louder or one octave lower than the smaller one before this second excursion limit is reached. This is where it is being damaged and making loud clacking noises.

      If you are not pushing them that loud that low, then these excursion limits don't matter.

      There are ways to calculate how much displacement is required if you want to play a 100Hz note at 85dB, to see if that would exceed the Xmax or Xlim of a driver you are considering.

      DISPERSION: The diameter of the larger diaphragm is about twice that of the smaller. This means that the frequency at which the drivers become effectively omnidirectional and the frequency at which they will “beam” will be about an octave lower for the larger one than for the smaller. This is relevant to their performance at the upper end of their band, not the lower, and how they integrate with a midrange or tweeter if you care about controlling dispersion for off-axis listening or for room reflections. Notice how the 30-degree-off-axis measurement separates from the on-axis measurement at about 1400Hz for the larger driver, compared to about 2200Hz for the smaller one.

      ACCELERATION: The “force factor (Bl)” of the small one is 7.3Tm, while the “moving mass (Mms)” is 18.5g. The ratio of motor power to the mass it has to control is thus .395Tm/g. This figure represents its ability to accelerate the cone. The larger one has a 13Tm motor trying to control a 112g cone, which is a ratio of .116Tm/g. This means that the smaller one can respond more quickly to transients, low-level signals, and higher frequencies. The ratio of force factor to “mechanical resistance (Rms)” is similarly in favor of the smaller driver. This advantage does not show up in a FR curve.

      The lighter cone also means it is probably less likely to keep moving from inertia after the electrical signal stops, which is another way speakers distort, and a reason why shorter excursion has less distortion.

      LOW-END LINEARITY: While the cabinet makes a big difference in how smooth the lowest frequencies of a loudspeaker are (and room reflections even more), I would worry about how ragged that low-frequency response is in the smaller woofer. It is easy to make a cabinet that introduces ugly FR problems; it is harder to make one that smoothes out problems inherent in the driver. Thus, to answer your question, I’d guess that no, the low-frequency response will not smooth itself out just because you put the driver in a cabinet. I’m guessing the engineers intentionally sacrificed some low-frequency linearity for the sake of an extraordinarily smooth and flat response from 150-1000Hz. Although they say the “operating frequency range” goes down to Fs, I think they really intend this driver to be used with a woofer below it to handle frequencies below 150Hz. Other 8-inch drivers on the market have smoother low-end response, indicating they are engineered to be used in that lower band.

      Some manufacturers publish harmonic distortion measurements, and they typically rise dramatically in the lower end of a driver’s frequency band. Scan-Speak does not give us that data, but I would expect that low-end distortion to start rising where the FR curve starts going jagged. The larger driver seems intended to be used in that octave below 150Hz. I would guess it has lower harmonic distortion down there. I don’t know how audible the difference would be. There is much debate about the audibility of harmonic distortion. But if it is audible anywhere, it is audible when generated by woofers, because the harmonics are in the midrange.

      I also notice that the output of the smaller driver starts to roll off below 100Hz, while the output from the larger driver stays flat to 30Hz. Presuming Scan-Speak measured the two drivers in the same baffle, this means that not only is the smaller driver less sensitive in general, it is even more less sensitive below 100Hz, which is another reason to think it is not engineered to be used down there. It would need equalization of some kind, if you want to use it all the way down to its Fs and keep it flat to 1000Hz.

      As billfitzmaurice mentioned, using multiple drivers helps when you need to make the output louder. This means that if you need to use equalization to boost output in the low-frequency band, it helps to have the increased displacement available as provided by multiple drivers.

      There have been some very respectable speaker designers (John L. Murphy and Roger Russell) who have used good 3” or 4” drivers for the entire frequency range, all the way down to 30Hz, but they have done so by using lots of them (25 in a vertical array), then using equalization to boost the low end as needed, because the total displacement of all those cones permits them to play loud enough down there. Equalization does not, however, eliminate harmonic distortion that is inherent in drivers being played at lower frequencies, but, as I said, there is debate about how audible harmonic distortion is.

      Trying to do that with 1-inch drivers would not work, because they probably don’t produce any sound at all at frequencies that the equalization would be trying to boost.



      • #7
        Smaller drivers 8inch and under IMO seem to have more mid bass bloom/grunt that I dont care for while 10inches and up have less of that mid bass which I prefer. For me I prefer a 2 way with at least a 10inch powered sub which basically makes it a 3 way. For bass frequencies I prefer larger drivers.


        • #8
          Moving air in an orderly fashion is like herding cats.

          You can do it in 3 ways,
          -Physically constraining the space
          -Using a large surface area
          -Using speed

          -Physical constraint would be like making the room smaller so the cats can't physically be dispersed over a larger area. (air constrained within a horn)

          -Large surface area would be like walking along with a large net to force the cats to move (large cone)

          -Or you can swoop in and grab each cat as quickly as you can and throw them in one spot before they disperse. (speed/small cone)

          Which scenario are you most likely to get bitten?


          • DrewsBrews
            DrewsBrews commented
            Editing a comment
            I know it is a very rough analogy (for simplicity, but mostly for the lolz) but that is essentially what I am getting at. I suppose I could have said that in a smaller/narrower room it is easier to get the cats to move in the direction you want. Cat impedance is a little more advanced than I wanted to go. ;D

            "but those pool cues can't grab enough water to do the job effectively, no matter how fast you row"... Depends on what you consider "effective" lol. Some folks might be perfectly smitten going .05mph while rowing furiously. Just like some folks are fine letting their small woofers handle the bass work.

            I'd say pool cues are a small cone, oars are a big cone, and constraining the water in a trough as narrow as whatever you are using for an oar is the throat of a horn
            Last edited by DrewsBrews; 08-04-2022, 02:07 PM.

          • mcargill
            mcargill commented
            Editing a comment
            i understand electrical resistance. It is measured in Ohms. I'm less clear about how Ohms compares directly to the kind of resistance we might measure in air. Do we attach the electrodes of the Ohmmeter to the air in front of the driver? Or do we use some other unit of measurement, in which case the comparable measurement of the "impedance" of the driver's diaphragm would be measured in some other way besides attaching the leads of an Ohmmeter.

            But that is not nearly the conundrum that CAT RESISTANCE presents. What units would we use to measure THAT? The Tabby? A highly compliant cat would be less than one Tabby, while a stiff-necked, stubborn cat would be more than one Tabby? Is a Siamese an order of magnitude more than one Tabby? Then a herd of cats could be measured in total Tabbies per cubic litter?

          • mcargill
            mcargill commented
            Editing a comment
            Apparently mcargill doesn't know what he is talking about. Impedance is not the same as resistance. You can measure resistance with an Ohmmeter, but not impedance. The resistance of a driver stays constant while the impedance curve shows how impedance varies with various sorts of reactive factors. For instance, the oscillating motion of the cone when it reacts by resonating causes a huge reactive force that impedes electrical flow around a specific frequency. And therefore one can read from the impedance curve the impeding effects of factors that would not have resistance measurable by an Ohmmeter.

            One such factor would be reacting volumes of confined air. They can impede cone motion, which would show up in the impedance curve for the loudspeaker. We measure the driver's inherent impedance in free air precisely because we want to eliminate any contributions from confined air. We can then measure by the impedance curve the effect of confined air in a loudspeaker, and measure it in Ohms. It is because, as billfitzmaurice says, the air in contact with the front of a direct-radiator diaphragm impedes the cone's motion so little that the impedance curve of a driver in a typical box speaker looks hardly any different from the curve for the driver in free air (until compression of the air in the box behind becomes a factor, at low frequencies). It is when the driver confronts resisting and reacting air volumes confined by compression chambers and horn throats that the effects of those air volumes can be measured in Ohms.

            I'm sorry I had to school you on this elementary stuff in public, mcargill, but you really should learn to keep your thoughts to yourself when you don't know what you are doing. If you can, that is, ever know when you do not know what you think you know. I think that is a question Socrates raised with Theaetetus, or with Meno, or somebody. Look it up.


        • #9
          I have four speakers:
          15" woofers (x2), 5" midrange, 1" tweeter
          7" woofer, 5" midrange, 1" tweeter
          10" midrange, seos horn (not a full range speaker)
          4" midwoofer, 1" midrange

          My opinion:
          15" woofers (x2) - Will fill up a room of any size. During the movie Kate on Netflix there are some gargantuan Japanese taiko drums being played. The drums truly sound like drums, full impact.

          7" woofer - The metal illuminator 18WU/4747T has 10mm of klippel verified x-max, superior to the paper version and 4mm beyond its specifications. In my bedroom it is 10db too hot all the way down to 20hz thanks to room gain. I use Dirac Live room EQ to bring the bass down and keep it neutral. It's not capable of filling a massive ranch style downstairs and they sound "small" but in a small bedroom it's 95% of the larger speakers. Its shortcomings are that even when flat to 20hz in a small room there is little visceral impact and it cannot render the Taiko drums accurately. In other words the bass is there but not something you can "feel" below 25hz in home theater despite going that low.

          10" midrange - When combined with a subwoofer it doesn't lose anything. WIthout a subwoofer pretty pathetic

          4" midwoofer - Add any subwoofer you want. It still sucks and sounds "small". I have not tried playing Taiko drums with a sub but the disappointment was memorable.

          What I have yet to find out:
          How will the 7" 18WU/4747T sound when crossed to a 15-18" subwoofer? We choose 80hz as a crossover point because below 80hz it is difficult to locate a speaker in a room. Bass frequencies go higher than 80hz so how much is missed (if anything) by using a 7" woofer from 80hz-250hz?


          • LewisH
            LewisH commented
            Editing a comment
            Thanks, thats very helpful to appreciate the less measurable aspects of musical sound. Im left wondering how 4 18wu/4747T's per cabinet would sound.

        • #10
          the 18wu models with max SPL above tuning frequency at 109dB with 60w input exceeding xmax

          The 32 models with max SPL above tuning frequency at 116dB with 150w input exceeding xmax

          the 32 has a greater xlim (22mm).

          So F3 aside - the 32W wins with headroom


          • #11
            Just to clarify the statements about horn loading, since most people are unclear. My 8 ohm compression drivers, when installed on 511 horns, are transformed into a higher impedance by the loading, 16 ohms at 400Hz, falling smoothly from there. The varying phase angle of the raw driver is transformed into something within a few degrees of pure resistive. That's because the diaphragm is being forced to do work against the air in the horn throat, unlike a cone driver which is almost unaffected by the air.