The mathematics of amplifiers

[LSM07]

The only thing that can be reliably deducted from the speaker diameter is how big the speaker is.

Might need AI verification on this...

 

[MechaSparky]

It's not necessarily louder, that's the first error it the logic.

There's WAY more to this than just driver size.

Also, using the nominal diameter for area calculations is misleading, only the moving part of the diaphragm (which is smaller) matters. A 10" driver has a diaphragm diameter of about 8.5" and a 15" driver is about 13.5".

I mean, he indicated that he was talking to a woman, so...

(juuust kidding - couldn't resist)

 

[toughluck]

However, I do think most audio engineers would agree that subwoofer systems are not designed to operate in the same frequency range as bass guitar cabinets, and therefore the design goals and designs trades would be different. Obviously there are physics/acoustics and electrical/audio engineering similarities being considered, but IME a good subwoofer would make a terrible bass cab (for most people) and vice versa.

The reason is because while many of the fundamental frequencies of the notes on the bass guitar do fall in a subwoofer range (in my mind for live sound approximately 100 Hz and below...and that is admittedly subjective), a lot of what we enjoy in a bass guitar note is in the second and third harmonic range and often higher, especially for playing up the neck and/or getting good articulation from some higher frequency definition to the notes.

I agree with what you said and I was stirring the pot by saying that bass cabs are essentially subwoofers but that's because the question in the original post was worded poorly.
Larger diameter and greater Xmax combine to higher swept volume. This allows a more capable speaker in a properly designed cabinet to produce higher SPL and lower frequencies.

A bass cab or combo is not a subwoofer of course because its design goal is to produce a broad frequency range. Optimally, it would produce a full range of frequencies and there will be no low pass filter to the main driver, so it will produce frequencies up to kilohertz range.
You're right that low frequency rolloff in a bass speaker starts at a higher frequency than in a subwoofer, which ideally goes as low as possible. A bass speaker doesn't go as low as a subwoofer and even though it produces low frequencies, it would make a poor subwoofer overall.

However, in terms of producing frequencies at and below a few hundred hertz, the design principles of a bass cab/combo and a subwoofer are the same. Cabinet design (sealed or ported), cabinet volume, port tuning, these considerations are the same for a bass speaker as for a subwoofer, with the caveat that the bass speaker doesn't need to go as low, so it can use a smaller driver and a smaller box and still be a great cab/combo.

 

[4-stringB]

I used to work with a drummer that flatly stated; " Tens are for bass, twelves are for guitars and fifteens are for vocals." You see? You guys are making this way too complicated.

 

[Bassdirty]

I used to work with a drummer that flatly stated; " Tens are for bass, twelves are for guitars and fifteens are for vocals." You see? You guys are making this way too complicated.

Like ya said, He was "a Drummer"...so, that kinda sets the premise.


JK, I also play drums.

T$

 

[jplunara]

Diameter alone does not really tell you which is louder. Loudness come from usable power and the sensitivity.

Usable power is the lower value between how much power the amp can deliver and how much power the speaker can handle. Use RMS or IEC power ratings. Ignore program power and peak power.

Sensitivity can be expressed a couple of different ways. The most common is to state the SPL measured at 1 meter when 1W is applied. For example Sensitivity = 97dB 1W/1m.

Some specs state the SPL measured at 1m when 2.83 Volts is applied. The trick here is to know that 2.83V applied to 8 ohms will result in 1W. So 97dB 2.83V/1m at 8 ohms is the same as 97dB 1W/1m. 2.83V at 4 ohms results in 2W. To convert to a 1W Sensitivity rating simply subtract 3dB. Sensitivity of 100dB 2.83V/1m at 4 ohms is the same as 97dB 1W/1m

Once you have the usable power and sensitivity stated at 1W/1m you can use this formula.

• Calculated SPL = 10Log(Usable Power) + SPL

Lets assume usable power is 350W and the Sensitivity of the cab is 97dB 1W/1m

Calculated SPL = 10Log(350) + 97 = ~122.4dB


The first part of the equation tells you the decibel change that occurs from raising the usable power from 1W to 350W.

Decibel Change 1- 350 = 10Log(350) = ~25.4dB.


So if you are comparing multiple speakers and the usable power stays the same, the cab with the higher sensitivity rating will be louder.

The specs will not always accurately compare cabs because there is no standard for how the specs are developed. They should be accurate when comparing two cabs from the same product line. They may not always be accurate when comparing cabs from different product lines, even if both lines are from the same company.


Example of 210 Vs 115 comparison.

Aguilar DB115

• Power Handling = 350W
• Impedance = 8 ohms
• Sensitivity = 96dB 1W/1m
• Usable Response 32Hz
• Calculated SPL at rated power = ~121.4dB

Aguilar DB210

• Power Handling = 350W
• Impedance = 8 ohms
• Sensitivity = 98dB 1W/1m
• Usable Response = 41hz
• Calculated SPL at rated power = ~123.4dB

So in this example the 210 should play noticeably louder but the 115 plays noticeably lower.

This is a great way to demonstrate the math, but the thread was totally lost at the conclusion. 2dB is definitively not noticeable. It takes at least 3dB to even register as an audible difference to the human ear.

 

[S-Bigbottom]

But it at least tells you that a 2x10 and a 1x15 are vaguely in the same area (sorry!), but a 2x12 is a fair bit bigger, but way smaller than a 4x10. The main takeaway, perhaps, is that more watts and more area is most likely to be louder, but more watts and less area may stay in the same sort of region.

4x10 = 40" and a 2x12 = 24", yet most modern 2x12 cabs perform the same or better than most 4x10 cabs. Depends of course.

24 is the same or better than 40 on some occasions.

 

[toughluck]

That's a naive sum of nominal diameters. Area increases as square of diameter, so you actually have 226 sq.in. vs. 314 sq.in., which is a 40% difference instead of 67%.
A 4×10" will have a dispersion pattern of a single ~20" speaker, while a vertical 2×12" will have a vertical dispersion pattern of a ~24" speaker and a horizontal dispersion pattern of a 12" speaker.

 

[logdrum]

CPA of 40 years here, what is important is the sensitivity of the cabinet (when measured accurately and consistently) the size of the drivers is meaningless

The size will affect cost of materials, manufacturing costs , the marketing strategy and the potential profit margin. Isn't that what CPAs calculate

Ultimately the bean counters have the final say after the marketing dept have massaged the spec sheet .

The best pairing I've heard is a 210 + 115. I've heard this in Mesa Subway and Bergantino versions. In both cases, the 115 seem to be more full range or more specifically more treble , high mid content.

I have a powered Bergantino 310 which is rated at 1000 watts

 

[Boneless]

This is a great way to demonstrate the math, but the thread was totally lost at the conclusion. 2dB is definitively not noticeable. It takes at least 3dB to even register as an audible difference to the human ear.

Untrue. The human ear can consistently notice RMS level differences of ~0.6dB. And it can notice lower level differences if paying close attention to them. At least in the midrange (let's say 1-3kHz). At lower or higher frequencies, it depends a bit on the listening level since our ears are less sensitive to them. And all of this is most valid within a certain SPL range (let's say centered around 80dBSPL, ±15dB).

 

[sawzalot]

It never ceases to amaze me how threads like this quickly veer from answering the question into the obscure but true and from there into the downright wrong. In terms of loudness the original post by @Wasnex captures it. There are edge cases too, which have been captured in the thread also.

But remember with musical instrument amplifiers, the amplifier is part of the sound creation, not just the sound reproduction and that's super important. So the bottom line for me: How does it sound to you? Being loud isn't everything. I LOVE the sound of a Mesa Subway 1x15. If it isn't as loud as a 2x10, I'm fine with that as long as it's loud *enough*. I've heard plenty of highly sensitive, very loud speakers that sound like crap. Sometimes you have to get out of the specs and just use your ears.

 

[ardgedee]

A 4×10" will have a dispersion pattern of a single ~20" speaker, while a vertical 2×12" will have a vertical dispersion pattern of a ~24" speaker and a horizontal dispersion pattern of a 12" speaker.

I can't believe that's possible because multiple speakers will have lobing and single speakers will not, and the lobe patterns will vary by frequency and number of drivers.

 

[Al Kraft]

Sometimes you have to get out of the specs and just use your ears.

Agree completely and I would say "almost always". I've played numerous amps and cabs that essentially had the same specs but sounded and felt (to me as player) totally different.

Sometimes specs will help you know whether to count something in or out especially if you know what your use case requires.

 

[agedhorse]

This is a great way to demonstrate the math, but the thread was totally lost at the conclusion. 2dB is definitively not noticeable. It takes at least 3dB to even register as an audible difference to the human ear.

The average player can pretty easily hear a 1dB difference at most frequencies.

 

[blr2]

The average player can pretty easily hear a 1dB difference at most frequencies.

True. At low to moderately high SPL, 1 dB is definitely audible, 2 dB is obvious.

 

[jplunara]

The average player can pretty easily hear a 1dB difference at most frequencies.

Well, alright... I definitely trust your judgement so I went down the small rabbit hole... Seems that old adage is completely wrong, made up.

Blind Testing a 1 dB Level Difference

Discover the smallest difference in level (dB) you can reliably hear.

www.audiocheck.net

1dB was easy, 0.5dB was a bit of a challenge, and I had mild but probably not statistically significant accuracy at 0.2dB.

When you're wrong, you're wrong.

 

[jthisdell]

The size will affect cost of materials, manufacturing costs , the marketing strategy and the potential profit margin. Isn't that what CPAs calculate

Ultimately the bean counters have the final say after the marketing dept have massaged the spec sheet .

The best pairing I've heard is a 210 + 115. I've heard this in Mesa Subway and Bergantino versions. In both cases, the 115 seem to be more full range or more specifically more treble , high mid content.

I have a powered Bergantino 310 which is rated at 1000 watts

Yes, I calculate s%$* like that all day long. Let's get together and talk about Doctor comp or Sec 754 inside/outside basis in partnerships sometime, lot's of fun.

I have a Berg CN112 and 210 and together they are pretty big.

 

[toughluck]

I can't believe that's possible because multiple speakers will have lobing and single speakers will not, and the lobe patterns will vary by frequency and number of drivers.

Considering dispersion, take it from the horse's mouth:

Cone size vs frequency response

Why nominal diameter tells you nothing about tone! When confronted with a statement that speaker diameter and tone / frequency response are independent the sceptic will ask, "Well why are PA subwoofers big speakers like 18" and why are hi-fi tweeters tiny 1" domes?" Good point, well presented...

barefacedaudio.com

Speakers will mutually couple if they are placed close to each other (close means closer to each other than half of a wavelength for a given frequency). An 8×10" array will nominally be 20"×40" (give or take a few inches), so frequencies below ~160 Hz will be sonically coupled (constructive interference will occur). Frequencies above 160 Hz will be a mess resulting from different interferences.

 

[agedhorse]

Well, alright... I definitely trust your judgement so I went down the small rabbit hole... Seems that old adage is completely wrong, made up.

Blind Testing a 1 dB Level Difference

Discover the smallest difference in level (dB) you can reliably hear.

www.audiocheck.net

1dB was easy, 0.5dB was a bit of a challenge, and I had mild but probably not statistically significant accuracy at 0.2dB.

When you're wrong, you're wrong.

There's so much bad info out there that it is hard to separate the truth from the fiction. This bad information gets fed into AI algorithms and perpetuated by those who don't do a deeper dive (like you eventually did). Good for you doing so too.

 

[agedhorse]

Considering dispersion, take it from the horse's mouth:

Cone size vs frequency response

Why nominal diameter tells you nothing about tone! When confronted with a statement that speaker diameter and tone / frequency response are independent the sceptic will ask, "Well why are PA subwoofers big speakers like 18" and why are hi-fi tweeters tiny 1" domes?" Good point, well presented...

barefacedaudio.com

Speakers will mutually couple if they are placed close to each other (close means closer to each other than half of a wavelength for a given frequency). An 8×10" array will nominally be 20"×40" (give or take a few inches), so frequencies below ~160 Hz will be sonically coupled (constructive interference will occur). Frequencies above 160 Hz will be a mess resulting from different interferences.

Dispersion (polar) pattern is one reason, but high frequency extension is another reason. Larger diameter drivers have much higher moving mass and far greater high frequency losses when optimized for low frequency response. With clever design, these can be mitigated to some degree, but that does require trade-offs in other areas.

When you say that frequencies above 160 Hz will be a mess, that's not in fact true. There may be some lobing in the polar pattern but in many cases this is a complete non-issue and can actually be preferred by players (mostly in large venue applications). This is partly why 410 and 810 cabinets are still considered one of the gold standards, because in REAL WORLD applications the sum of the trade-offs just work the best.

Arraying speakers can also be used to another advantage, the constructive and destructive interference can be used to intentionally modify the polar pattern of a single point source by adding additional point sources to achieve narrower dispersion in one direction or another. It's not entirely bad or a mess.