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Thread: Formula Wanted

  1. #1
    Senior Member Ducatista47's Avatar
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    Formula Wanted

    This is just for my curiosity, sort of, but does anyone have a formula for calculating the energy needed to produce sound at different frequencies, dB's being equal? I suspect low frequencies contain (relatively) enormous energy and need big watts to produce them, but I haven't found a formula to quantify the relationship yet.

    I'm using a 300 watt amp for 290hz on down and six tube watts above, and it seems about right. I would like to see what mathematics has to say about it.

    I am also curious about the whole HT sub thing. I want to see some science applied to the choice of amplification there.

    Also, a somewhat related topic: when a master line level volume control is used, what is the best position for power amp volume? I use about eleven o'clock. This is all about headroom and tone, of course.

    Clark in Peoria
    Information is not Knowledge; Knowledge is not Wisdom
    Too many audiophiles listen with their eyes instead of their ears


  2. #2
    Senior Member Ian Mackenzie's Avatar
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    Clark,

    Its fairly involved so don't worry too much about it.

    A good analogy is cubic inches for low end power..cone area that is.

    300 hz is about the split for 50/50 share of actual power on music signals.

    Your 6 tube watts will go reasonably for average listening but for HT would might need more power, valve amps clip gracefully..!

    If you turn the Lpads up to +3 this will provide 3 db increase in sensitivity. Just turn down the volume on the small amp by the same amount and this will provide 3 db more headroom.

    I should add that the first watt is the most important in the midrange and Hf region and your amp being a good valve rig probably has a lot to do with why you are enjoying your 4345 so much.

    No need for a sub with the 4345's.

  3. #3
    Senior Seņor boputnam's Avatar
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    Quote Originally Posted by Ian Mackenzie
    No need for a sub with the 4345's.
    Ian got that trick question right! You have TWO "Master Class" subs there. I've never heard anyone's "subs" match the impact of the 2245H's...
    bo

    "Indeed, not!!"

  4. #4
    Senior Member Ducatista47's Avatar
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    OK, OK, I should have been less (does anyone know a formula...) or more specific.

    I have no crazy desire to ever use subs for music. If I'm ever feeling let down by the 2245's, I'll have my ears cleaned or commit myself. Bo, you speak the truth, and from experience. I have never even heard of let alone heard a music woofer better than the 2245H.

    I happen to know that I have at least 10x music headroom from my little tube amp. I've proved it here before. No clipping here. Ian, HT is indeed the magic word here.

    The non-idle part of my curiosity is wondering what energy would be required to propagate, say, a 16hz wave at sturdy volume, as compared to a 30 hz or 300 hz wave. Obviously, not from a 2245H in a 4345 enclosure. Mind you I have two dead cores I could have reconed. Perhaps one spare and one for an HT sub enclosure someday. But I suppose there are better woofers for that.

    Ian, you are as usual spot on about valve amps, the first watt (Im convinced I have one of the very best - see http://audioheritage.org/vbulletin/s...ad.php?t=11575 ), and your L-pad suggestion is a very sweet idea, thank you.

    You are of course both spot on about the 4345 needing a sub issue.

    Still, you know what? I am really curious for curiosity's sake. If either of you feel like boring me with the complexities of the answer to my mathematical quest, please steer me in the right direction or blackboard it in a PM. One thing is for sure, you are both great friends and I again thank you for including me in your spheres.

    Clark in Peoria
    Information is not Knowledge; Knowledge is not Wisdom
    Too many audiophiles listen with their eyes instead of their ears


  5. #5
    Senior Member Ian Mackenzie's Avatar
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    Clark,

    16 hz properly is an ask, and if it was used for music it would sound like crap most likely. Using conventional wisdom you are talking lots more 2245's and lots of room real estate and lots of power.

    In an old speaker builder book there is a graph of 1 acoustic watt versus frequency, its a square law or something like that. Check out Steve Schell's large horn loaded 515's for other approaches.

    The 4345 is good down to 30hz, maybe a bit lower with room gain. 30 hertz might not sound low but the 2245 will do it without compression or 2nd or 3rd harmonic distortion. You can get the 2245 to go lower but that means a much bigger box with eq and it might not sound very good for music, use < 80 hz only.

    It basically a dead issue for music , for HT maybe but in a small room it would not be worthwhile unless you were on top of the sub where the energy is radiated globally.

    You are best to arrange a JBL 1500 or other specialist sub for VLF.

  6. #6
    Senior Member Ducatista47's Avatar
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    I have the 5235 set at a 30hz cutoff, as recommended by JBL. I can't be missing much. I was amazed at how low 30 hz sounds on a stereo test cd. Heck, 50hz was way deep. I'm sure deep bass rounds out the tone, though.

    You remind me, Ian, that my 24 x 15 x 8 foot room cuts off at about 23hz anyway. What was I thinking? Even if a 16hz wave can only be more felt than heard, it wouldn't propagate in my playroom anyway. Still, I'm going hunting for that chart or the formula that generated it. Thanks for the tip.

    You know, since I have found most special effects driven movies to be complete dung as films, I would probably not miss the sub in a HT setup anyway. Like another member said before, we have plumbing to pipe the crap out of the house. Bone shaking synthesized tones are no sub-stitute for directors' craft, acting, cinematography and writing. When I spot a model-turned-actress staring in a film aimed at teenagers I run the other way. It is not the effects that make or break a film's quality. I'll give Spielberg's War Of The Worlds a ten and Pearl Harbor a minus six. For the stated reasons.

    Clark
    Information is not Knowledge; Knowledge is not Wisdom
    Too many audiophiles listen with their eyes instead of their ears


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    Hi, Clark,

    I believe you're referring to the Equal Loudness Level Contours, more commonly known as the Fletcher-Munson curves, which give an approximation of the frequency-dependant sensation of equal loudness;

    The lowest curve is the minimum audible level of sound. As noted, the ear is most sensitive around 2-5 kHz. To be audible at this same minimum level, a sound at 20Hz must be 80 dB (100 million times!) more powerful than a sound at 3 kHz.

    Of course, variables like room gain/boundary effect and such tend to render poor application predictability, though new methods are greatly improved.

    The accurracy of the curves has been in debate since their creation in 1933, resulting in the 2003 modified version for ISO standards. More on that here;

    http://www.aist.go.jp/aist_e/latest_.../20031114.html
    Attached Images Attached Images  

  8. #8
    Senior Member Ducatista47's Avatar
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    Thank you, Moldyoldy, I see from the new curve that the peak sensitivity at 4000hz did not go away yet! Looks like we were designed to hear our own speech, rustling twigs, a few predators and the odd screaming volcanic vent. Score one more for evolution.

    I think my energy question's exact answer may lie in a further investigation (by ignorant me) of what a dB really means, and how it was developed. The answer is probably built into the unit; otherwise the formula I seek would be basic knowledge for tranducer designers. Give me a longer life and I will discover more of my ignorance.

    Clark
    Information is not Knowledge; Knowledge is not Wisdom
    Too many audiophiles listen with their eyes instead of their ears


  9. #9
    Senior Member JBLnsince1959's Avatar
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    Ducatista47:

    here's a book that might help you - Master Handbook of Acoustics..by F. Alton Everest

    also, One thing to consider...Once you get to a certain point on the musical scale ( the lower notes on a piano and below) those notes are mostly preceived by their harmonics and NOT the fundamental note itself ( which is why a good tight-but-full midbass is important or why Rusnzhana heard a big difference in my PS series bass when we stuff the 800's)...going super low is cool for movies and that push against your chest and vibration in your seat..but not needed for music

    I agree with what you said about movies

  10. #10
    Senior Member LE15-Thumper's Avatar
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    Quote Originally Posted by Ian Mackenzie
    Clark,

    300 hz is about the split for 50/50 share of actual power on music signals.
    I am not sure what you mean by this Ian.

    Are you saying if you biamp at 300hz you should have equal amounts of power for the High and Low frquencies ?:dont-know

    He clearly has much more low end power than high end power, I realize that bass requires much more power. I thought at 300 hz 6 watts wouldn't really cut it as far as keeping up with the bass end of things.
    LE15-Thumper
    "Give me JBL, or give me death"

  11. #11
    Senior Member Ducatista47's Avatar
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    Quote Originally Posted by LE15-Thumper
    I am not sure what you mean by this Ian.

    Are you saying if you biamp at 300hz you should have equal amounts of power for the High and Low frquencies ?:dont-know

    He clearly has much more low end power than high end power, I realize that bass requires much more power. I thought at 300 hz 6 watts wouldn't really cut it as far as keeping up with the bass end of things.
    It's the 30hz, not the 300hz that needs the power. If one assumes x10 headroom, that figure goes from 0.5 watt to 5 watts at 300hz. At 30 hz both figures would be many times more. My original question of watts needed vs frequency given constant perceived dB was so I could quantify the difference.

    Also, the upper stage of the 4345 has a 3dB bump in efficiency over the 2245H. That alone is another x2. (I think?)

    Now Ian can give a more intelligent answer, I'm sure!

    Clark in Peoria
    Information is not Knowledge; Knowledge is not Wisdom
    Too many audiophiles listen with their eyes instead of their ears


  12. #12
    Senior Member Ducatista47's Avatar
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    Quote Originally Posted by JBLnsince1959
    Ducatista47:

    here's a book that might help you - Master Handbook of Acoustics..by F. Alton Everest

    also, One thing to consider...Once you get to a certain point on the musical scale ( the lower notes on a piano and below) those notes are mostly preceived by their harmonics and NOT the fundamental note itself ( which is why a good tight-but-full midbass is important or why Rusnzhana heard a big difference in my PS series bass when we stuff the 800's)...going super low is cool for movies and that push against your chest and vibration in your seat..but not needed for music

    I agree with what you said about movies
    Thanks as always! I live in a university town, I should be able to find the book.
    Movies - I'll give The Whole Wide World a ten plus ten, and it has no special effects I am aware of.

    Clark
    Information is not Knowledge; Knowledge is not Wisdom
    Too many audiophiles listen with their eyes instead of their ears


  13. #13
    Senior Member Phil H's Avatar
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    Ducatista
    JBL has a sound design manual online that may interest you. Part one (of two) has a couple formulas.
    Part 1: http://www.jblpro.com/pub/manuals/pssdm_1.pdf
    Part 2: http://www.jblpro.com/pub/manuals/pssdm_2.pdf

  14. #14
    Administrator Mr. Widget's Avatar
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    RE: 300 hz is about the split for 50/50...

    Quote Originally Posted by LE15-Thumper
    I am not sure what you mean by this Ian.

    Are you saying if you biamp at 300hz you should have equal amounts of power for the High and Low frquencies ?:dont-know
    Yes, that is what he is saying.... I have a chart somewhere that shows the relative power requirements for audio dividing the spectrum into four frequency bands... can't remember specifically what it said but the 300Hz 50/50 thing seems to be roughly in line with what I recall.

    Back in the 70's, following the chart I placed my 250wpc amp on my woofers that crossed over at 100Hz, my 100wpc amp on the midbass (100Hz-1000Hz), and my 40wpc amp on top... I was into loud and quickly discovered that with the musical content of the day, I needed more power in the 100Hz-1000Hz range and less below 100Hz so I switched my 100wpc amp with my 250wpc amp. Back then there was little material with content below around 40Hz. Those '60s and '70s rock albums and even the symphonic pieces just didn't place much deep bass on the records.

    Back to your question about the 50/50 split of power usage, I think Bo uses a pair of identical amps on his 4345s... I am sure that it varies with program material but it might be interesting to find out if both of his amps are being driven approximately equally. Since the 2245 and the 2122 have similar sensitivities (with the compression drivers being padded down to match) it would be a good test of the idea.


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  15. #15
    Senior Member JBLnsince1959's Avatar
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    Quote Originally Posted by LE15-Thumper
    I am not sure what you mean by this Ian.

    Are you saying if you biamp at 300hz you should have equal amounts of power for the High and Low frquencies ?:dont-know

    He clearly has much more low end power than high end power, I realize that bass requires much more power. I thought at 300 hz 6 watts wouldn't really cut it as far as keeping up with the bass end of things.
    I'm not sure I understand that either...must have lost something in translation...

    Usually you need more power for the lower notes in raw wattage. however, the area 300 to 5000 is VERY IMPORTANT in how we hear what we hear...also one reason why our ears are so sensitive that high ( most of our speaking fundamentals are below 1000) is that , that's where a lot transients and lower harmonics lie and we pick up alot of information from that area. Transients need a lot of headroom (sometimes 100's time more power)

    Good luck with your search..... It will be interesting what you discover.....

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