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Wavelength of the low B

Discussion in 'Miscellaneous [BG]' started by fretlessman71, Mar 22, 2013.

  1. Says here that a low B is approximately 30.4 Hz, and that the wavelength is over 36 feet. So how come I can hear it sitting right by the amp? Am I just getting overtones or something?
  2. acmebass

    acmebass Commercial User

    Mar 22, 2013
    Englewood, CO
    Owner/Designer, Acme Sound/Acme Low B
    Form the same reason you can hear bass when you wear headphones. The ear doesn't respond to "waves," it responds to instantaneous pressure changes at the eardrum.

    It's been a longstanding bit of mythology that it's necessary for a space to be large enough for the complete waveform to "develop" in order for it to be heard or reproduced, but in fact, that's just silly. If it were true, you wouldn't be able to hear any frequencies below, say, 4000 Hz through your headphones.
  3. You are usually hearing harmonics from the note. Few cabinets can reproduce 30Hz well. The first harmonic of the low B is 60Hz and lots of bass cabinets can handle that.

    I had a cabinet once that was designed to have a -3dB point at 30Hz and this was verified with some RTA equipment. It had two 18s in it and was the size of a chest freezer. It used to be part of my friends PA system that he built himself. He used it for a couple of years and then bought an even bigger system. I had the cabinet in my house and used it as the subwoofer in my home theater. It was awesome ! I would play Korn's first album and some of Fieldy's low B-string notes would shake the entire house.
  4. This is half true. The myth that the length of the low frequencies is why you should listen from a distance is silly, but the "myth" holds true since different frequencies aren't emitted with the same amount of directionality.

    Low frequencies are less directional then higher frequencies, and they travel through materials (like the walls or the floor) easier. If this wasn't true, then if you were playing in the middle of a large carpeted room, your amp should sound the same whether or not you're standing in front or behind it. Unless you're dead center in the line of fire of your speaker's cone, what you hear in front of your amp isn't very representative of what the audience hears. Tilt-back speakers and (to a lesser degree) tall stacked speakers (like an SVT) give the player a better representation of what the audience is hearing because the higher frequencies are emitted in more of a straight line to your ear.

    Of course, there's other factors (like the room shape, wall materials, if there's a PA reinforcing the bass, how many people are in the audience, etc.) that may be far bigger factors to altering your sound. However, the rule of thumb of stepping off 20-30 feet is good to figure out how you may sound to the audience works well in most situations (based not on wavelengths, but on a distance from which the directional higher frequencies spread out to better match the more omni-directional lower frequencies).
  5. acmebass

    acmebass Commercial User

    Mar 22, 2013
    Englewood, CO
    Owner/Designer, Acme Sound/Acme Low B
    Absolutely right, Ubersheist, but you're sort of addressing a different question than I was, or than he asked.

    Just as a point of clarification, the directionality at a particular frequency is related to the ratio of the wavelength to the size of the source.

    So, are low frequencies "less directional?" Well, sort of, because at low frequencies the source is relatively small compared to the wavelength. But if the source is large, say greater than half a wavelength, the wave becomes increasingly more directional. In the real world this isn't much of a concern, of course, because very few speakers are that huge, so this is mostly a theoretical concern. But it's true!

    The actual relationship looks like this: sin x=1.22*(W/D), where x is the angle of dispersion, W is the wavelength, and D is the diameter of the source.

    As you can see, there is no "low" frequency defined or specified, but rather only a ratio of wavelength to source.

    Nice funky thing you have happening there, BTW. Better drummer than I am, and nice bass sound, too! Hope y'all have some good gigs.
  6. acmebass

    acmebass Commercial User

    Mar 22, 2013
    Englewood, CO
    Owner/Designer, Acme Sound/Acme Low B
    Excellent real-world observation, Vince.

    As usual, I come from a point of theoretical absolutes, and despite the fact that there are some commercially available cabs which can reproduce the low B note with great authority and low distortion, I'm afraid you're pretty much right on the money in most cases.
  7. Allow me to say that I LOVE the discussion, and am learning a lot. You have my permission to deviate from the OP when you feel it pertinent to the concept at hand. :D
  8. To the OP:

    Your ear doesn't pick up on how long the sound wave is, because they move at 760+ miles per hour.

    Let's look at an analogy first - pretend you take tickets at a subway entrance or a football stadium. There's a long line of earthworms and snakes that are coming through the gate, but the line moves at the exact same speed as someone walking. Let's say the first customers that come in are a bunch of earthworms. You can see them lined up, and can see how long they are, but more importantly, you can get 100 of them in through the gate every minute. The next customers are some 50-foot long massive pythons. You can't see the start or the end of any one of the pythons, as just one python's too long to see around the corner of the hallway. However, you at the gate can see that it's a 50' python because you can only get one of them through the gate in a minute even though the line is moving at the same speed. It's sort of similar with your ear.

    Your ear picks up how fast the air pushes back and forth on your eardrum. So, at 30 hertz, your eardrum gets pushed in and sucked out 30 times in one second, and your brain deciphers that as one really long, big sound wave. A crash cymbol's foundational note may be around 5000 hertz (I'm guessing, can't remember off hand). As such, your eardrum gets pushed in and sucked out by the air 5000 times in one second. Our brains can decipher this difference, and computes them into two different sounds.

    That's interesting. I never really studied the physics of sound on a theoretical level other then maybe one or two weeks in a Physics 101 class in college.

    So, let me ask you how does multiple speakers factor in with regards to frequency response? I always heard that it was directly related (and maybe even somehow directly proportional) to the surface area of the speakers.

    Here's what I've noticed with regards to cabinets' responses to low B strings - an amp with one speaker 12" or less doesn't handle the low B very well. 15" speakers handle it OK, and an 18" speaker handles it just fine. However, that Phil Jones cabinet with 21 of the 5" speakers handles a low B no problem, and is super clear.

    Any insight or thoughts about that?
  9. My immediate thought is that it has less to do with the size of the speaker, and more to do with the amount of air being moved and/or the size/efficiency of the cabinet...?
  10. Okay... did a little math. The area of 21 5" circles is about 421 sq. inches, whereas a single 18" circle yields about 254. I bet this has a lot to do with it.
  11. acmebass

    acmebass Commercial User

    Mar 22, 2013
    Englewood, CO
    Owner/Designer, Acme Sound/Acme Low B
    Well, your explanation using the subway and the critters is certainly unique, and I never would of thought of it, but I don't think I have a problem with it!

    With regard to low end extension, ironically, I find myself between Vince, who observes that a great many cabs have trouble in the area of low frequency reproduction, and rightly so, and you, Ubersheist, as you tend to agree, even while you point to a cab which seems to be an exception to the general rule.

    While I an loathe to comment on another manufacturer's work, I will emphasize that while none of us are immune to the laws of physics, large drivers are better for low frequencies, small drivers are better for high frequencies, careful design work can often surprise us, and I approve of your use of the word "handle," as opposed to the word I used. Reproduction of fundamentals at frequencies below the resonance of the driver is always devilishly difficult.

    That said, Hofman's Iron Law is probably worth a look: http://www.glasswolf.net/papers/hoffman.html

    (I actually have the definitive piece on Hofman's Law, written by Henry Kloss, in my files, which I intend to add to the "Archives" section of my website, but haven't gotten it done yet.)

    FYI, in response to a question from a customer, I wrote some words pertaining to the use of a greater number of smaller drivers for reproducing low frequencies a few years back. I hope you can view it in the "Forum" section of my website, but you might not be able to- the site is undergoing revisions. But that should clarify a few things.

    Suffice to say there are certain ideas which seem to be resurrected with each new generation of audio buffs, which don't seem to stand up to the test of time. Yeah, I'm sort of old.

    Here is a link to a page on the site of a true giant of loudspeaker design, Roger Russell, on which he discusses his experience with a popular design from 1961, referred to as the "Sweet Sixteen." (Scroll down.) http://www.roger-russell.com/columns/columns.htm
  12. acmebass

    acmebass Commercial User

    Mar 22, 2013
    Englewood, CO
    Owner/Designer, Acme Sound/Acme Low B
    You're into about ten things at once, Fretless. I'll leave that to someone else. The link to Hofman's Iron Law, which I provided above, might be helpful for starters.
  13. Wow - leave it to me to overthink stuff. I didn't go to college; I went to music school. Therefore all physics I know and understand are observation-based...

    Of course, reproducing 31 Hz requires that you actually HAVE a signal that has a frequency of 31 Hz (something many 5 strings simply fail at)...

    ....hey, MY thread, MY tangent. :spit::smug:

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