A Question on Speaker Driver Efficiency


I have been tweaking my guitar amps, by upgrading the speakers.

I installed a larger speaker (was 8" now 10") in my bass amp, but I made sure it was very efficient - net result
- not only is the bass much deeper sounding,
- but because the new driver was more efficiant I now play at a lower volume.

So I am now considering upgrading my other amp (i.e. used for my 6 string) and got to thinking about building a new cabinet that houses two speakers.

I know that connecting the speakers in ...
- series will double the impedance, i.e. 2 x 4 ohms would have an onverall impedance of 8 ohms
- parallel will halve the impedance, i.e. 2 x 16 ohms would have an onverall impedance of 8 ohms

But what I have not been able to get my head around is...
- what will each connection method (i.e. series or parallel) have on the "combined" sensitivity rating?
- e.g. if both speakers are rated at 96db sensitivity, will the overall sensitivity change due to the connection method or remain at 96db?

Since I can get 4 ohm or 16 ohm drivers - which connection method would be best? series or parallel?

in case it is a factor
- the amp is 15 watts into 8 ohm
- I am looking at employing two identical drivers each rated at 96db sensitivity
- 96 db (or higher) is the target for the combined sensitivity

Any help is appreciated - Many Thanks Steve
williewonka
Each is not absorbing 1/2 watt when placed in series (with the required 2.83 V applied) and the net acoustical sum of output is approximately 97db - not 94db. Two obvious errors in one sentence. The math doesn't lie and frankly, I'm getting a little tired of the verbal gymnastics at this point. The math is simple and anyone who wants to read the details above can readily see where the error was established. Yeah, you can double the input drive voltage to 5.7v and then the series arrangement will have each woofer dissipating 1/2 watt. You can also multiply the input voltage by 10,000 - it won't tell us anything about the effect placing two identical drivers in series has.
@almarg  Its pretty evident to me that this guy seems to equate '1 watt' with '2.83v' and so is somehow assuming that I meant '2.83 volts' when I was pretty talking about the power (not voltage) being '1 watt'.

Also his intuitive grasp of Kirchoff's Law seems to be weak, and I further find that talking about capacitance when dealing with 2 guitar speakers as opposed to one rather silly, since any such distributed capacitance on the coils (or anywhere else) is going to be quite low and negligible. But even if it was not, in a series connection current would have to flow through both drivers in order for one to work. For all his 'hand waving', he seems to have no grasp of the formulae he presented, how they are used or their significance. 

@kijanki +1


@cj165
I'm sorry, I would call you by name, but I haven't seen it posted.  I came very close to sending this in a private message, but much has been addressed in this thread as well as a couple of others. 
1st... You are extremely knowledgeable and could be if you chose to be, a very strong contributing member to this forum. I personally would love to see that happen. 
You have 7 pages of responses, I did not count the threads, but I would guess maybe 8 or 10.  In those threads I read maybe 20 or so of the post.  In each thread at some point, you belittled someone. 
Odd that one of your threads, you discussed heavily forum etiquette, I believe the thread was discussing if someone needed to prove that they were qualified to chime in on these forums.  
I would say that 98 percent of the members here come here to learn and share the passion of their hobby.  All of us at some point get challenged with our knowledge and being the he men that we are, we seem to have to defend ourselves (except maybe Elizabeth and you attacked her also). I'm not sure if you are trying to prove something or are insecure in yourself that you have to feel superior over others?  Really, I'm not try form a conjecture.  I am really hoping that you are here wanting to contribute and would take it serious that we are all people, all have feelings and all want to be treated with respect. There is no doubt, that I have said stupid things on this forum that can and have been challenged, On the other hand,  there is no doubt, that I have made a difference and contributed to others personal audio issues.  Your knowledge in most area's of audio make my knowledge a pittance,  but I can tell you if the disrespect continues, I will turn you off.  I appreciate your knowledge level and am hoping to appreciate you personally for your contributions.  
I am trying to say all of this in respect.  
Tim (timlub)  
This was posted on another thread today.  I don't think that he is 100% wrong, but the problem of his delivery does not seem to sink in.  Its everyone else. 
@cj165 ... with my pea brain, I had to look up fiefdom syndrome. Thanks for the education there. I picked a few things from your rant for you to consider. 
1. You have not been scorned or ridiculed because  you challenged the resident experts.... You are correct, you are scorned, but it is because of your disrespect.... Overall,  I loved the debate,  Your contribution will cause many people to start studying to get to the last nitty gritty that separated your opinions in the debate. 
2. Others "Command Respect because of their post count"  Their is no Command... I assume that you are referring to Al & Ralph.  They both regularly contribute in a way that has helped countless people solve technical issues in their own systems. 
3. "Followers implore moderators to ban the newbie"   That could get worse, its up to you. I don't believe that anyone would want you to change your opinion and sharing facts.  Its all in the presentation. 
4. "Causing issues to constantly being revisited"  Yes,  issues are often revisited, but it is because, they come up every so often for different people and are often addressed as they come. It has nothing to do with Impeding Technical progress. 
Everyone,  Here is his post from this morning, See Below: 

" Some Audiogoners (no names) start threads after threads which ask the same questions, over and over and over again. They usually get thoughtful responses, but they, the OPs, don’t seem to learn anything or have the motivation to act on any of the thoughtful responses. At best, "they" seem confused or maybe have too much time on their idle hands. " - ps
In Audiogon forums, the ratio of the clueless soothing their fragile egos with endless hand waiving nonsense to the knowledgeable citing proven science and mathematical evidence tends to be pretty high. This scenario is clearly not restricted to Audiogon alone. A high percentage of forums possess posters who "command respect from followers" simply because they have several thousand posts under their belt. The fact that most of their contributions have been hand waiving BS intentionally or unintentionally misleading others doesn't seem to matter. The "reputation" and "belief system" are all that counts. And when a newcomer or "unknown" hits the scene with "facts from the big bad world outside", he/she is often scorned, ridiculed, challenged for credentials, or in egregious cases - the "followers" implore moderators to ban the newbie if the newbie presents facts that disagree with the "grand proclamations of resident forum experts". The end result is often persistent ignorance, in many cases, this ignorance persists with basic fundamental subjects that "in the big bad world outside", have been settled long ago and are considered trivial. This fiefdom syndrome is made worse when utterly unqualified salesmen are allowed to pitch their products without any deference to science or facts. The mere fact that they've been pitching the same old garbage for 30 years is supposed to be enough for the "followers" and sadly in many cases, it is. So just as it is with other forums, at Audiogon, there are a significant number of influences that impede technical progress - causing issues to be constantly revisited that should have been settled long ago.
This is exact quote from cj1965 post:

In theory, half the voltage applied to a driver will result in half the sound pressure in the output (-3db).

Thanks, Kijanki.  Here's another interesting quote, this one from the thread Tim referred to above:

CJ1965 4-19-2018
For some people, "results" means using antiquated 80 year old technology that is highly vulnerable to changes in performance depending on what it's connected to. And for some folks, the lack of bass and exaggerated highs, coupled with increased harmonic distortion when using this ancient "technology" is "pleasing" or "desirable". Similarly, others see the pops and ticks, rapid wear, uneven high frequency performance, limited dynamic range, increased distortion, wow, and flutter associated with ancient vinyl technology as "more authentic". Unfortunately, we can't confine such individuals who promote and buy this junk to padded cells. We pretty much have to create invisible "padded cells" that effectively allow ourselves to ignore them.

Best regards,
-- Al
 
This is exact quote from cj1965 post:

In theory, half the voltage applied to a driver will result in half the sound pressure in the output (-3db).
Res ipsa loquitur, huh?

Obviously he didn't actually do the math, but based this on belief instead- the exact thing of which he was accusing others...


For a single driver : The change in dB in input voltage is equal to the change in output SPL in dB.

Voltage dB can be calculated in this fashion: 

dB = 20 x log ( Vnew / Vold )

in the case of half the voltage:

20 x log ( 1 / 2 ) ~= (- 6 dB)

Also, you can use this handy web gizmo:

http://www.sengpielaudio.com/calculator-gainloss.htm
Also, we are so far from the OP's original topic, maybe we should let this thread just die. :) 
@cj1965 and other Respected and Valued contributors to this forum. cj1965 is obviously well schooled in the math, a stickler for precision, and interested in the truth of the matter. I believe/hope his knowledge “could” become valued here. However, “manners” are vital in order to become a “respected and Valued” member of any reasonable group. “Anyone” can have a misstep or slip up. We’re human. Such an event “does not” necessarily diminish one’s value or credibility. I’ll mention Ralph here as he is known to produce exceptionally listenable and prized audio equipment under the ATMASPHERE label; and is without doubt a valued contributor. 
However, harsh criticism, or sarcasm, is “generally recognized” as a deliberate attempt to demean a person.
Reasonable and compassionate people will/may react to defend the person(s) subject to the personal attacks. 
This has occurred here. 
I don’t support a ban of the offender at this time. He may have been having a “bad day(s) for reasons unknown. I do believe apologies are “generally accepted”; and are a good response to a correction of a error in a “statements of fact”, even if semantics are causing the misunderstanding, as well as for “personal insults”. Unfortunately, insults are more unacceptable than factual errors(which can always be corrected!). Insults, even if based on accurate facts, cannot be corrected. They linger in the minds of all. I highly recommend the high road of, at the minimum, a general apology for insulting comments. And best wishes to all. Peter
@erik_squires 

No, we're not far off from the essence of the question posed by the OP. Application of the decibel expression of voltage gain/loss to sound power gain/loss is not appropriate..

Sound power level, denoted LW and measured in dB, is defined by

LW = 10 log 10 ( P/P 0 )   d B

not 20 X log 10(P/Po) db as you suggested above.




 
... not 20 X log 10(P/Po) db as you [Erik] suggested above.
CJ1965, Erik did not say that or suggest that.

He said 20 x the logarithm of the ratio of applied voltage, not 20 x the logarithm of the ratio of power. If half the voltage is applied power will be reduced to 1/4 of the original amount, resulting in a 6 db reduction in SPL according to your own 10log(P/Po) formula, which is correct. And that is what Kijanki was implicitly pointing out when he quoted your erroneous original comment on the matter.

Also, and more significantly, +1 to the very well said comments above by Peter (Ptss), which together with the earlier comments by Timlub I suggest that you (CJ1965) would be well advised to take to heart.

Regards,
-- Al

Thanks @almarg - I should have said "voltage" a few more times I think. 

Best,


E
@almarg 

Please look up the definition of sound power. You will find it is not based solely on the net force applied but the area as well. If you run the calculations for sound power and put the values in the sound power db formula, you will get -3db. The graph below the calculator on the website Erik linked to also indicates this (voltage gain/loss  is-6db while, sound power is -3db).

The formula or calculator for voltage gain/loss is not supposed to be used for sound power. One has force units the other power - apples and oranges.
.
Assuming that a speaker is operating in a reasonably linear manner, meaning for example that it is not being over-driven to the point that thermal compression becomes significant, it seems to me that the relation between acoustic power out and electrical power in will remain constant to a close approximation. And electrical power in will be proportional to the square of the applied voltage.

Therefore it would seem to me (and I believe also to Erik, Atmasphere, and Kijanki) that since a 50% reduction in applied voltage will result in a 75% reduction in electrical power in, which corresponds to a 6 db reduction in electrical power in, the result will be a 6 db reduction in acoustic power out.

Regards,
-- Al

@cj1965

Where in my post did I mention power? I mentioned the relationship between output dB and input voltage.

Having said that, as @almarg has alluded, both formulas are true. Much like

P = V x I

and

P = (V x V) / R

They are mere re-writing of each other. Again, I encourage you to grab XSim to validate any formulas. It is pretty accurate. 

Best,

E
Al - Yes indeed. These are all just rewrite.  Since power is proportional to the square of the voltage:

(0.5 x 0.5) = 0.25

Now, calculating power difference: 

10 log (0.25) = -6 dB

Calculating voltage difference:

20 log (0.5) = -6 dB

In either case, the SPL at a reference distance, measured in dB, changes in proportion to the power OR voltage when either is expressed as dB assuming there is no compression in the driver. 

Said another way, for a single driver:

Delta V dB = Delta W dB = Delta SPL dB

That's what's so cool about dBs! 

Best,

E
Cj1965 has made mistakes. Just shows he’s no different than anyone else when it comes to knowledgeable discussion.
Here’s hoping he’s at least bright enough-from an EQ perspective- to realize he wouldn’t enjoy belittling, condescending, or harshly critical comments directed as a personal attack on him. If he is “bright” enough he will reflect on his “petty” attempts at personal disparagement and get on with his sincere apology. Man up. If he doesn’t apologize he’ll be remembered (forgotten) as an inconsiderate, tiny minded( as he just couldn’t see the big picture) cretin, who could do a bit of math-but not always correctly :(
I get particularly displeased when a person is graciously made aware of a shortcoming— but carries blithely on.
I was taught that’s a true true sign of real ignorance. 
Al - Yes indeed. These are all just rewrite. Since power is proportional to the square of the voltage:

(0.5 x 0.5) = 0.25

Now, calculating power difference:

10 log (0.25) = -6 dB    - erik_squires

Wrong again. You cannot simply substitute the electrical power ratio into the sound power formula and call it a day.

The ratio of measured sound power to reference sound power is 1/2 - not 1/4. And if you multiply the area factor in the formula for sound power in a medium, the ratio goes back to 1 - yielding 0 db. And with that, I’m done giving out free lessons in first year electrical engineering. Find someone else to insult.
Sorry, wrong is wrong. And with that, I have to move on. I have better things to do with my time.

And with that, I’m done giving out free lessons in first year electrical engineering. Find someone else to insult.

Well I must say some days a much more interesting here than others. :)

E
Life is always interesting. Here again we have the one who is most insulting - to be the most sensitive... aw , darn shame ain’t it ...
CJ1965 4-20-2018
Wrong again. You cannot simply substitute the electrical power ratio into the sound power formula and call it a day.

The ratio of measured sound power to reference sound power is 1/2 - not 1/4.
I posted the following in this thread, into which this debate had spilled over:
Almarg 4-21-2018
Regarding the debate about the relation between SPL and speaker input power, I found the following sub-page at the site which provided the calculators that were referred to earlier:

http://www.sengpielaudio.com/calculator-efficiency.htm

Entering various parameters into either of the two calculators closest to the bottom of that page (one entitled "Sound Pressure Level and Amplifier Power" and the other in the section entitled "Electro-Acoustic Sensitivity") clearly confirms what Atmasphere, Erik_Squires and I have all said on this subject. Namely that if the input power to a speaker is changed by a given number of db, SPL at a given listening distance will change by the same number of db. (As previously stated, this of course assumes that the speaker is not being driven hard enough to cause thermal compression in the drivers to become significant).

I also found the following writeup at PSB’s site, which provides additional confirmation. About 2/3 of the way down the page a table is provided showing power vs. volume for an unnamed 87 db speaker used as an example. Note that 40 watts results in a volume of 103 db, while a 6 db reduction in that power level (to 10 watts) results in a volume that is 6 db less (97 db). While a 3 db change in power, from 1 watt to 2 watts, changes the volume by 3 db, from 87 db to 90 db. And a 20 db change in power, from 1 watt to 100 watts, changes the volume by 20 db, from 87 db to 107 db.

http://www.psbspeakers.com/articles/Guide-to-Speaker-Specifications
Regards,
-- Al