Ohms, volume, watts, and stuff

[SteveFreides]

I'd appreciate a brief primer on how some of this stuff works. (One thing I do know is that speaker resistance varies with frequency, but I'm hoping we can leave that out of this discussion and just assume a flat resistance across the frequency spectrum.)

I own an AI Ten2, whose internal speakers are rated at 4 ohms.

If I hook up a matching extension cabinet (Ten2-EX), 2 things happen that I'm aware of: first, I have twice as much speaker area producing sound, so that will make it louder; second, the resistance seem by the amp drops from 4 ohms to 2 ohms, and the power rating at 2 ohms is about twice as high. I have no idea what the change in power rating actually means in the real world. Is it, e.g., that instead of getting 400 watts into 4 ohms, I'm getting 400 watts into each of the 4 ohm speakers and _that_ and only that is why it's louder? What if I hooked up a dummy 4 ohm load that didn't produce any sound - would my Ten2's output be louder driving that 2 ohm load?

I'd also like to know what the consequences would be, specifically to what comes out of my Ten2, if I add a _different_ extension cabinet. E.g., I have a Contra-EX, also 4 ohms, which I think is less efficient - does that mean that if I hook up the Contra extension speaker, I'm getting whatever extra sound it can produce in addition to what comes out of the Ten2 but the Ten2's output remains unchanged?

Last, what if I had an extension cabinet that was as effficient, driven by itself, as the Ten2's internal speakers, but was rated at 8 ohms? What would change, if anything, about what came out of the Ten2 when the extension cabinet was hooked up, and what would be different coming out of the 8 ohm cabinet by itself as compared to when it's hooked up _with_ the Ten2's speakers?

Part of why I'm asking is just that I'd like to understand more and better, but another reason is purely practical - if I add a non-matching extension cabinet, the last thing I'd want to do is make the output of the Ten2 itself worse in any way, and I don't know if that's what happens with a 8 ohm extension speaker or with a less efficient 4 ohm speaker like the Contra-EX.

Many thanks in advance.

-S-

[longfinger]

While we're at it, can someone explain why amps are measured by "wattage". Is this about power consumption? If the technology is more efficient, should not more sound come from less watts consumed?

[GrowlerBox]

Originally Posted by SteveFreides

I'd appreciate a brief primer on how some of this stuff works. (One thing I do know is that speaker resistance varies with frequency, but I'm hoping we can leave that out of this discussion and just assume a flat resistance across the frequency spectrum.)

I own an AI Ten2, whose internal speakers are rated at 4 ohms.

If I hook up a matching extension cabinet (Ten2-EX), 2 things happen that I'm aware of: first, I have twice as much speaker area producing sound, so that will make it louder; second, the resistance seem by the amp drops from 4 ohms to 2 ohms, and the power rating at 2 ohms is about twice as high. I have no idea what the change in power rating actually means in the real world. Is it, e.g., that instead of getting 400 watts into 4 ohms, I'm getting 400 watts into each of the 4 ohm speakers and _that_ and only that is why it's louder? What if I hooked up a dummy 4 ohm load that didn't produce any sound - would my Ten2's output be louder driving that 2 ohm load?

I'd also like to know what the consequences would be, specifically to what comes out of my Ten2, if I add a _different_ extension cabinet. E.g., I have a Contra-EX, also 4 ohms, which I think is less efficient - does that mean that if I hook up the Contra extension speaker, I'm getting whatever extra sound it can produce in addition to what comes out of the Ten2 but the Ten2's output remains unchanged?

Last, what if I had an extension cabinet that was as effficient, driven by itself, as the Ten2's internal speakers, but was rated at 8 ohms? What would change, if anything, about what came out of the Ten2 when the extension cabinet was hooked up, and what would be different coming out of the 8 ohm cabinet by itself as compared to when it's hooked up _with_ the Ten2's speakers?

Part of why I'm asking is just that I'd like to understand more and better, but another reason is purely practical - if I add a non-matching extension cabinet, the last thing I'd want to do is make the output of the Ten2 itself worse in any way, and I don't know if that's what happens with a 8 ohm extension speaker or with a less efficient 4 ohm speaker like the Contra-EX.

Many thanks in advance.

-S-

Paging drurb .....

In the meantime, I may be able to offer some pointers.

1. With the matching extension cabinet, as you have pointed out, there are two primary changes -- the power output has more or less doubled as a result of the impedance drop, and the speaker cone area has doubled. Each of these factors increases the sound pressure level (SPL) by approximately 3 dB, which is a clearly audible but not substantial increase, to a total of 6 dB, which is substantial. Note that to double the volume as you hear it coresponds to a 10 dB increase in SPL, which can be achieved by increasing the power output 10-fold through a speaker that can handle the increase, or through multiple doublings of your speaker area; doubling twice to a total of 4 speakers in this case will increase the SPL by around 9 dB, and beyond this things become somewhat less efficient (I think 2 dB for the next double). In most cases, of course, a combination is used. In addition, as long as the centres of your cones are less than half a wavelength apart (as they typically are for bass frequencies), there is further reinforcement of those sounds, heard as better bass "extension". And, still further, if your cabinets are stacked with the speakers arranged vertically, there is the advantage of having a speaker nearer your ear, and also no loss of dispersion of frequencies in the middle and higher ranges on the horizontal axis.

2. By adding a dummy load, you simply waste (as heat) a part of your output in proportion with the resistance applied; you will gain exactly no advantage.

3. With non-matching extension cabinets, things are more complicated. By not matching impedances, you simply "shunt" more current towards the lower resistance. If the higher-impedance cabinet is much more efficient, it may keep up, but there is a risk of damaging the other cabinet with too much current. If impedances match, but one speaker is much less efficient, then it will add relatively little to your volume, and may rob you of your hard-earned tone by producing certain frequencies out of phase with the other speaker, resulting in unpredictable cancellations and reinforcements, heard differently in different parts of the field. If you're lucky, this can work well, but it can be an expensive experiment. More reliable to match cabinets. If you already have these extension cabinets, though, there's no harm in trying them out - just be sure to move around the room so you can hear them from various angles, and listen out for the aforementioned peaks and troughs.

4. As to why amplifiers are rated by power, that's at least partly a marketing thing. Voltage swing across the output terminals would make more sense, but it's not as sexy.

[drurb]

Please allow me to add a few comments and correct a few points in your, overall, fine answer. I hope my comments will be accepted in the spirit in which they are intended... which is a desire to help people understand.

Originally Posted by GrowlerBox

Paging drurb .....

In the meantime, I may be able to offer some pointers.

1. With the matching extension cabinet, as you have pointed out, there are two primary changes -- the power output has more or less doubled as a result of the impedance drop, and the speaker cone area has doubled. Each of these factors increases the sound pressure level (SPL) by approximately 3 dB, which is a clearly audible but not substantial increase, to a total of 6 dB, which is substantial. Note that to double the volume as you hear it coresponds to a 10 dB increase in SPL, which can be achieved by increasing the power output 10-fold through a speaker that can handle the increase, or through multiple doublings of your speaker area; doubling twice to a total of 4 speakers in this case will increase the SPL by around 9 dB, and beyond this things become somewhat less efficient (I think 2 dB for the next double). In most cases, of course, a combination is used. In addition, as long as the centres of your cones are less than half a wavelength apart (as they typically are for bass frequencies), there is further reinforcement of those sounds, heard as better bass "extension". And, still further, if your cabinets are stacked with the speakers arranged vertically, there is the advantage of having a speaker nearer your ear, and also no loss of dispersion of frequencies in the middle and higher ranges on the horizontal axis.

Doubling the area of the cone does not, in and of itself, increase the acoustic output. So, there aren't two 3-dB effects, each adding up to 6 dB. Several factors are being mixed here. Let's begin with one speaker cabinet. We'll assume that it's being driven with a given voltage, say, 1 volt. If we add an identical speaker cabinet in parallel, then the impedance "seen" by the amplifier drops in half. This will require the current to double if the amplifier is to maintain that 1v across both speaker cabinets. If the amplifier is capable of supplying that current, it will be supplying twice the power. Assuming that the speakers are driven in phase, and measuring at a point equidistant from the two cabinets, there will be an increase of 6 dB in acoustic power. Depending upon the specific frequency and distance from each cabinet, one will measure an increase in power less than that. Measure at a point where the waveforms are out of phase and you get no output at all. Considering the cabs as independent sources, you'll get an increase of 3 dB overall.

Now, largely because the impedance of speaker cabs is many times higher than the internal impedance of solid-state amps, there is nothing even close to maximum power transfer (that's a geeky detail). The effect that results is that the amp is actually able to supply more power (up to a point!) into a load of lower impedance. So, if your amp is rated, say at 400 watts into 8 ohms and 800 watts into 4 ohms, you actually CAN develop more power from it at the lower impedance. So, yes, hook up an 8-ohm load and the most you can squeeze from it is 400 watts; connect a 4-ohm load and you can get 800 watts. In the example above, if you hook up the second cab, you will actually get 3 dB more power and (considered independently) 3 dB more acoustic output.

Originally Posted by GrowlerBox

2. By adding a dummy load, you simply waste (as heat) a part of your output in proportion with the resistance applied; you will gain exactly no advantage.

Precisely. Consider the example above. Suppose you hook up an 8-ohm resistor in parallel instead of the second cab. Assuming the first cab to act like an 8-ohm resistor (which it doesn't but we'll assume that for simplicity), you'll still get that 400 watts developed across the cab and another 400 watts developed across the resistor that you can use to help heat the room.

Originally Posted by GrowlerBox

3. With non-matching extension cabinets, things are more complicated. By not matching impedances, you simply "shunt" more current towards the lower resistance. If the higher-impedance cabinet is much more efficient, it may keep up, but there is a risk of damaging the other cabinet with too much current. If impedances match, but one speaker is much less efficient, then it will add relatively little to your volume, and may rob you of your hard-earned tone by producing certain frequencies out of phase with the other speaker, resulting in unpredictable cancellations and reinforcements, heard differently in different parts of the field. If you're lucky, this can work well, but it can be an expensive experiment. More reliable to match cabinets. If you already have these extension cabinets, though, there's no harm in trying them out - just be sure to move around the room so you can hear them from various angles, and listen out for the aforementioned peaks and troughs.

Yes, but there isn't really a risk of damage as a result of "shunting" current. As for what happens with combining different cabs, you may like this.

Originally Posted by GrowlerBox

4. As to why amplifiers are rated by power, that's at least partly a marketing thing. Voltage swing across the output terminals would make more sense, but it's not as sexy.

No, not at all. Power amplifiers are current sources, not voltage sources. What's important about a power amp is how much current can be supplied to a given load. If you know the impedance of the load, then you know the power. So, it's easier to quote the spec in terms of power into a given load because that's what counts. Think of it this way, your iPod can supply voltages (into loads made for it) quite near what your power amp can. Now, connect an 8-ohm load to your iPod and try to drive it and the problem is that it won't be able to keep up with the current demand, which will collapse the voltage.

Finally, speaker impedance, not resistance, varies with frequency.

[GrowlerBox]

Originally Posted by drurb

Please allow me to add a few comments and correct a few points in your, overall, fine answer. I hope my comments will be accepted in the spirit in which they are intended... which is a desire to help people understand.

Of course . And thanks once again (and doubtless not for the last time) for the corrections and clarifications.

[SteveFreides]

Originally Posted by drurb

Let's begin with one speaker cabinet. We'll assume that it's being driven with a given voltage, say, 1 volt. If we add an identical speaker cabinet in parallel, then the impedance "seen" by the amplifier drops in half. This will require the current to double if the amplifier is to maintain that 1v across both speaker cabinets. If the amplifier is capable of supplying that current, it will be supplying twice the power.

So, in the example of adding a Ten2-EX to a Ten2, without changing the volume controls on the Ten2, adding the second speaker requires the amp to deliver twice "umph" - forgive the non-technical term, please - so that the same "umph" is delivered to both the internal and extension speakers as was being delivered to only the internal one.

Originally Posted by drurb

And then we're looking at what happens with you take a given speaker producing something and have an identical speaker produce the same thing, which results in an audible increase in volume although one most people would describe as less than a doubling of the volume they hear.

Got it. My musician's analogy to this - I suspect it works not the same but along the same lines - is the violin section (or, for that matter, the bass section, or a chorus of voices). One violin makes a certain amount of sound, but two violins doesn't make twice the sound, and 24 violins doesn't make all _that_ much more sound than one, certainly nowhere near 24 times as much.

How'm I doin'?

Originally Posted by drurb

Finally, speaker impedance, not resistance, varies with frequency.

Could you explain the difference? I found this

"Resistance is a concept used for DC (direct currents) whereas impedance is the AC (alternating current) equivalent. "

Does this mean that because sound is a waveform, its ups and down (as seen on an oscilloscope) make what's coming out of the amplifier effectively AC, like wall current?

-S-

[fdeck]

Originally Posted by SteveFreides

Does this mean that because sound is a waveform, its ups and down (as seen on an oscilloscope) make what's coming out of the amplifier effectively AC, like wall current?

Yes. It's a time-varying signal, which is typically described as a mixture of AC signals of different frequencies and amplitudes. The particular mixture corresponds roughly to the tones and overtones produced by your bass. And the different frequencies "see" different impedances in the speaker.

However, in my view, for the sake of assembling systems from amps and speakers, treating the rated impedance as a resistance for the sake of calculation is a good rule of thumb.

[drurb]

Steve,

Your post contains a quote attributed to me regarding "volume." I assure you (and everyone else) that I did not write those words.

Moving on...

Originally Posted by SteveFreides

So, in the example of adding a Ten2-EX to a Ten2, without changing the volume controls on the Ten2, adding the second speaker requires the amp to deliver twice "umph" - forgive the non-technical term, please - so that the same "umph" is delivered to both the internal and extension speakers as was being delivered to only the internal one.

Basically, yes.

Originally Posted by SteveFreides

Got it. My musician's analogy to this - I suspect it works not the same but along the same lines - is the violin section (or, for that matter, the bass section, or a chorus of voices). One violin makes a certain amount of sound, but two violins doesn't make twice the sound, and 24 violins doesn't make all _that_ much more sound than one, certainly nowhere near 24 times as much.

How'm I doin'?

Well, two violins do produce twice the acoustic power of one! Twenty-four violins do produce 24 times the acoustic power of one. Powers add linearly. That's the physics. Now, we must take into account how the auditory system works. The auditory system, like other sensory modalities, basically appreciates ratio changes that can be thought of, for purposes of this discussion as logarithmic changes. Thus the decibel. Twice the power is 3 dB [10*LOG₁₀(2)]. Now, with those two violins, if you want to get another 3 dB, you need to go to four violins and so on. The increase produced by 24 violins over one violin is 13.8 dB [10*LOG₁₀(24)]. As Growler noted, if we move to the psychological attribute of "loudness," we find that it requires a change of about 10 dB (ten times the power) for human listeners to judge a sound to be twice as loud. By the way, the psychological attribute of "volume" is not the same as the attribute called "loudness." It's too bad that, somewhere along the way, someone decided to label amplifier gain controls as "volume."

Originally Posted by SteveFreides

Could you explain the difference? I found this

"Resistance is a concept used for DC (direct currents) whereas impedance is the AC (alternating current) equivalent. "

Does this mean that because sound is a waveform, its ups and down (as seen on an oscilloscope) make what's coming out of the amplifier effectively AC, like wall current.

Yes, such waveforms are "AC" waveforms. There are two components to impedance. There is the resistive component and the reactive component. The former can be thought of as how resistors behave (makes sense). Their resistance does not change with frequency. The reactive component is well represented by what occurs with capacitors and inductors. The degree to which those devices "impede" current flow varies as a function of frequency.

Loudspeakers, having wound coils, are basically inductors. Add a cabinet and perhaps a crossover, and you have what is effectively a system that can be modeled, electrically, as a network of inductors and capacitors. The 8-ohm rating of a speaker cab is little more than a general descriptor of the impedance, often in the mid-frequency range. Impedance can, depending on the design, vary radically with frequency. In the hi-fi world, having a power amp with high current capability is quite desirable because it's possible that the "8-ohm" speaker system you might want to drive dips down to 2 ohms at some low frequency.

Now, isn't this fun?

[spydr]

So here's another scenario that I use.
I have an Eden D410xst (8 ohm, 104db @1w1m) and a D210xst (8 ohm, 103db@1w1m). The idea was I could take 2, 4, or 6 10s to the gig based on loudness, load in, or other needs.
I'm not sure of the actual work load on each speaker when stacking the cabs with the amp bridged.
Am I working the speakers in the 210 harder than the 410's?
The amp is an Eden WT1205.
Should I run the amp bridged or split and balance adjust?

[GrowlerBox]

Yes, you are working the speakers in the 210 harder than those in the 410, as each cabinet will receive half the output if they are simply run in parallel from a single source. If you have the wherewithal to run each cabinet from a separate power section in your amplifier; that is, not bridged, but split and balance adjusted, you will run a significantly smaller risk of damaging your 210.

[Zoa]

In addition to you working the 210 speakers twice as hard, they are not going to be nearly as loud as the 410, assuming the sensitivity is relatively normal. Essentially, you're risking a lot (blowing your 210 if you turn up too loud) for not much gain in loudness.

[spydr]

Thanks guys.
I may explore ditching the 410 for a matching 210 for the flexibility and easier load-ins. Maybe even adding a 3rd 210 if needed.
On the other hand, I love what I get out of my 410.
Any opinions on 2 2x10s (8 ohms each) vs. 1 4x10 (8 ohm)?

[Zoa]

well, you will get more power with 2 210s, because that will be a 4ohm load vs the 8ohm for the 410. Also, you can stack them vertically, which gets rid of the dispersion problem inherent to 410s. Other than that, it depends on the individual cabs and personal preference.

[spydr]

Thanks guys for the valuable input.