Formula Wanted

[Ducatista47]

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

[Ian Mackenzie]

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.

[boputnam]

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...

[Ducatista47]

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/showthread.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

[Ian Mackenzie]

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.

[Ducatista47]

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

[moldyoldy]

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_research/2003/20031114/20031114.html

[Ducatista47]

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

[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

[LE15-Thumper]

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. :hmm:

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.

[Ducatista47]

I am not sure what you mean by this Ian. :hmm:

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

[Ducatista47]

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

[Phil H]

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

[Mr. Widget]

I am not sure what you mean by this Ian. :hmm:

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.


Widget

[JBLnsince1959]

I am not sure what you mean by this Ian. :hmm:

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.....

[Ian Mackenzie]

Hi,

What I was referring to was the share of power being split for biamping.

Ideally both amps should be identical in power but that is not a cast iron rule for home use.

In the old red book of Altec system designs annd Bozak among others there is a whole chapter that deals with Clark's question.

Its all about producing 1 accoustic watt at 50 hz in that Chapter so someone may have it and care to post some details.

[JBLnsince1959]

Hi,

What I was referring to was the share of power being split for biamping.

Ideally both amps should be identical in power but that is not a cast iron rule for home use.

.

That sounds better...I understand what you were saying now, thanks...

Just now saw Widgets answer also...

[Zilch]

http://en.wikipedia.org/wiki/Fletcher-Munson_curves

http://www.sengpielaudio.com/Fletcher-MunsonIsNotRobinson-Dadson.pdf

According to Dickason, the original 1933 curves are "now considered more accurate than the later Robinson-Dadson study done in 1953."

Interestingly, the recently reworked ISO 226:2003 curves depart even further from the originals.

If Dickason is correct, A-Weighting, based on the original 40 Phon curve, under-reports perceived bass SPL at any higher level.

As the Wikipedia reference points out, it's one reason contemporary recording EQ is sometimes FUBAR.

Same with loudspeakers. Voice to 80 dB, and it'll boom their brains out at 100.

Voice at 100, and it's "Weenie" below that.... :D

[rgrjit8]

I remember that chart. I believe someone posted it on the old heritage site that crashed. I've been trying all kinds of key words searching and haven't found a thing.

I recall that 250hz or, as has been mentioned, 300hz was the break even point for amplifier power.
In additioin, 800hz, was the point of a 1:4 ratio of power.

Some math genius can perhaps, derive a formula from this.

[Chas]

An interesting question you raise here, Clark. My personal thoughts on the subject of adding a sub to the 4345's are:

1. Distortion reduction. There is no doubt in my mind regarding the 2245H: it is, without doubt, a more than very capable transducer for normal residential use to the normal limits of low frequency reproduction. BUT, IMHO, if I can relieve it of sub 50 Hz modulations, I end up with a cleaner, more articulate bass. Personally speaking, this is important. Especially on jazz recordings. (Hello Charlie Haden?)

2. I (and others here, I'm sure) happen to prefer deep bass info and transients that are delivered via a closed box versus vented.

3. I play a lot of vinyl and, at times, crank up some really old records that are anything but flat (i.e. too many parties and too much heat from sitting on top of an old Pioneer Spec 2 power amp:p ). This inevitibly leads to infrasonic crap at high levels that can easily put a vented woofer into shock without a subsonic filter. I just hate hearing voice coils slam into immoveable objects......:banghead:

4. Position flexability. I can place my 4345's and subs for best individual performance. Less overall compromises that way.

[glen]

Same with loudspeakers. Voice to 80 dB, and it'll boom their brains out at 100.
Voice at 100, and it's "Weenie" below that.... :D
Hence the loudness button!
Once you understand the need for it, it seems remarkable how few amps and receivers included a continuously variable loudness control instead of a simple button.

[Mr. Widget]

...it seems remarkable how few amps and receivers included a continuously variable loudness control instead of a simple button.A proper loudness compensation is continuously variable but is turned on by a simple switch... that's why it is called loudness compensation instead of simply a bass contour. As you turn up the volume the amount of bass and treble added to the signal are reduced... at high volume settings the signal is flat.

Of course they are ball park approximations based on a set of assumptions. Since they can't know the sensitivity of your speakers or the power and sensitivity of your power amp if on a preamp, they are not really accurate... Most quality preamps do not offer this feature as it is assumed that you will be listening to the system at higher than "background" levels... and since the '70s most audiophiles prefer a simple signal path.


Widget

[John]

A proper loudness compensation is continuously variable but is turned on by a simple switch... that's why it is called loudness compensation instead of simply a bass contour. As you turn up the volume the amount of bass and treble added to the signal are reduced... at high volume settings the signal is flat.
Widget

Not on Marantz amps from the 70's:D

[Mr. Widget]

Not on Marantz amps from the 70's:DIf they don't change the amount of boost with increases in amp gain, then they aren't properly designed. My dad's Fisher was definitely variable as was my old Kenwood.

It's kind of funny... Back in the day I owned a Marantz 3800 preamp and I don't recall if it had a loudness contour or not. The damn thing had something like 500 buttons on it.... I traded up to a Threshold with four knobs and no loudness contour.:D I guess I never missed not having it.


Widget

[Ducatista47]

One of the reasons I purchased my Marantz 1152DC way back was the advanced loudness contour control. It wasn't continuous, but it sure had a lot of detent positions. The published curves enticed me and it delivered. Another piece in the "now dead but can't bear to throw it out" category. It was my main amp for many years, my first integrated amp to replace my separates, which included a 3300 preamp.

Clark in Nostalgia, Illinois

[DavidF]

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

I read your concern as whether the power of 6 watts being enough on the HiPass side and not the 300 watts on the low side. I wouldn’t think you could track down a simplified math model to provide a true answer or if you really need to. With so many variables involved (music or program material, type of music, efficiencies of speakers, xover configuration, amps over volts, power over current, and so on) you could work up quite a dissertation only to realize your ears can tell you what you need to know.

I too recall the 300Hz equal Hi and Lo break point. Seems like it would very a general type conclusion. I guess this to be talking about average power so as you decrease the break point, power requirements for the HiPass moves up considerably (and woofer requirements decrease considerably). So for your situation, power requirements for the HiPass is the same as the LoPass and your 300/6 ratio is a concern. IF 300 watts is needed for the LoPass then 300 watts is needed for the HiPass. Oops. But if 10 watts is OK for the LoPass because of system efficiency, then the 6 watts on the HiPass does not look so bad. You would want good power (or current) reserves for low-end transients so the tendency think high power is needed on the low end. But then, we are more sensitive to distortion in the mid and high range, so reserves are important there as well, yes?

I would go with what I hear. If you overdrive the Tubes-on-HiPass to the point you hear them cry, then you have your answer.

I wonder if there is a city out there called Nostalgia, somewhere?

DavidF

[Zilch]

If they don't change the amount of boost with increases in amp gain, then they aren't properly designed. My dad's Fisher was definitely variable as was my old Kenwood.Another scheme had separate loudness and volume controls, which I never understood.

I think I have an old HH Scott receiver here with that. Maybe I find it and measure.... :thmbsup:

[Hoerninger]

Another scheme had separate loudness and volume controls, which I never understood.
In theorie it's simple: With volume you control the sensivity (only once) and with loudness you control how loud you listen at the moment. My BRAUN REGIE 510 has it.
My old GRUNDIG had a combined loudness-volume control which i preferred, because it had a steeper bass attenuation, the rest was done with bass control.
____________
Regards
Peter

[Ducatista47]

I didn't mean to imply that I NEED a 300 watt UREI to power the 2245H's. I am USING it to power them because I have it and I like the amp a lot. I have become a fan of tight solid state low end (and sweet single ended small tube upper frequency), so I swapped my 60 Watt tube AB amp for the 6260. It fried itself, so I called up the 6290 (mit fan, Mein Herr!) to take over. So...300 watts. I think the 60 tube watts were enough by plenty, but I looked for a different sonic signature and found it. I didn't mean to imply the need for anything close to a 300 watt high current amp, so I was likewise not implying the need to match it up on the high pass. What I listen to and the way I listen to it needs no such power, but I like the solid state JBL/UREI sound.

That said, I still have a feeling that 30hz needs way more power for headroom than 300hz. Like I said, I was just trying to quantify it. I think it is the really low frequencies that need the serious power when push comes to...err...pull!:D While it is in theory possible to be too rich or too thin, it may end up being even more difficult to have too much low end power. Too much low pass power may be an oxymoron. Since it is in reserve, what's the harm?

Anyway, this is only a clairification about the 300 watt figure. I am really, really enjoying all the knowledge the responses to this thread are bringing to the surface. Please continue!

You guys are awesome, Clark

PS About the six watts. I know it is difficult to believe how a Grommes PHI-26 can sound so great driving the tops of the 4345's, but what can I say. You need to hear it yourself. Good luck finding a better sounding amp. Alan Kimmel is a genius. If you had one you wouldn't care what the numbers said either. Versatile, too. On headphones, including my power hungry Stax electrostatics, OMG. Alan explains the design not as producing no distortion, but producing no noticeable distortion that is audible to the human ear.

When their salesman was shopping it around, he came into a high end shop and announced it would make the most difficult to drive speakers in the place sound better than any other amp in the shop could. The journalist in attendance reported a no contest victory for the tiny Grommes. They haven't made even twenty of them yet. No one seems to know they are out there. Hint: Everyone I demoed it to wants one or has one now. I use the kind of audio shop that lets you take stuff home and try it. If you can find one of the thirteen dealers you might want to have a listen. Even with the JJ EL-84's it comes with, it sounds great. Tube roll and it will blow you away. (Mr. Kimmel recommends 6P14P-EV's. I wouldn't bother messing with the Sovtek 6N1P, it seems perfect.)

[Mr. Widget]

While it is in theory possible to be too rich or too thin, it may end up being even more difficult to have too much low end power. Too much low pass power may be an oxymoron. Since it is in reserve, what's the harm?I'd say that in general I agree with you... all things being equal. However, I would rather have a great 100wpc amp on bass than a mediocre 300wpc amp. (I am not pointing to anyone's amp :D)

All that aside, it really depends on the driver sensitivity and the source material you listen to. Chamber music will require orders of magnitude less power at the same SPL as will Hip Hop.


Widget

[Ducatista47]

Right on, Widget. I'm sure if I tried lots of amps I would find ones I would like better than the 6290. Not bad for a "PA" amp, though. Its greatest advantage over amps I don't have is that I do happen to have one right here!;) I suspect one of two things. Either it excels at bass frequencies and low down does not have the coloration you heard , or I am a tin ear and can't hear the difference. If I a/b'd it with other units, there would surely be differences. If someone gave me a Krell, it would sound great. I wouldn't pay many dollars for it, as above bass they sound seriously awful to me.

I wonder where Sun Ra falls in the Chamber Music / Hip Hop continuum?

Clark

[Ducatista47]

Since I was linking to a DEC paper in another thread, here is one explaining how 1.8 SET watts from the right circuit can drive difficult loads.
http://www.decware.com/watts2.htm

Notice that the remarks about clipping refer to it occuring in some applications, but not in mine, for instance.

Also note the letter is in response to an engineer and true blue meter man trying to bust Steve's balls. Julian Hirsch lives on, I guess.

Try this one, too, if you like.
http://www.decware.com/paper43.htm

Clark in peoria

[Ian Mackenzie]

I agree with the Widget.

Amps can sound sound considerably different on the upper bass region, often milky or grey sounding or lacking definition. In terms of low bass some amps can sound artificially tight and fail to impart the scale and dimension of the recording environment.

The 2245 is a very accurate transducer with a great blend of speed, pitch and linearity. It will easily impart the characteristics of you amps and signal path.

Talk to Guido about his new Aleph 2 clone on what reall bass sounds like.

In your senario Clark I would steer in the direction of articulation and refinement. Turn you L pads (when they are back up and going) to +3 on the mid, -1 on the Hf and slot then turn up the bass amp +3 db also.

The valve amp will have more reserve headroom.

Ian

[moldyoldy]

An important but often overlooked variable in this equation is damping, both the damping of the particular speaker, (integral as well as installed) and the ratio of the driving and driven impedances.

Generalizations seem to be the norm regarding damping, which can lead one to incorrect conclusions. It really should be considered on a per-application basis, especially when combining old tech with new.

For instance, bench tests of a particular tube amp may show flat or, more commonly, falling LF response, yet when connected to an assumed-flat speaker system shows raised LF acoustic output that can't be attributed to room modes. While you may perceive the increased bass to be a positive attribute of your tube amp, it's actually just distortion caused by the amps inability to fully control cone motion. Amps utilizing negative feedback can be optimized for particular damping requirements by varying the amount of feedback.

[Ducatista47]

Well spoken, Moldyoldy. One good thing about using exactly one possibly mid-fi 300wpc, full complementary, hugely transformered 6290 on exactly two 2245h woofers is exact damping. It's like the regenerative braking capability on a GE Dash 9. The power available to control motion is enough by plenty.

I am still looking into high(er)-fi replacements, but it's not bad now. Bass is really controlled and tight. Next to the Grommes tube amp on top it does suffer from lower clarity, probably the symtoms Ian described.

I only use the little tube amp on the rest of the system.

Clark in Peoria