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Underpowering speakers. Is there a ratio?

In general there is no such thing as underpowering a speaker. You can however, damage a speaker (tweeters mostly, very little chance of damaging a 10" driver) from clipping the amp. Know how when you turn a stereo (or your bass amp) all the way up and it sounds distorted? That distortion is the amplifier "clipping". In short, you are trying to make the amp produce more power than it can and the output becomes distorted. Technically, the waveform is clipped, and that's why it's called "clipping." That clipped waveform can hurt tweeters. Highly unlikely to hurt 10's or larger.

So in short, unless you play your 250watt amp wide open for about a week straight, there's pretty much no chance you will hurt your new cab. Hope this helps.

I endorse this message.

The important thing to consider is that a clipped waveform can contain more power than your "rated" output, more like 2.5x, and a lot of this power is in high frequencies. So there's a danger to tweeters any time you start letting your rig distort, no matter what the ratings. But in reality, you'll notice the distortion long before you get to this power, and you don't have tweeters. The risk is exactly the same with a perfectly matched setup--if the stage volume is too loud for you to hear yourself, you can't hear the distortion either, and now you've blown your tweeter. From this, we learn that you should never "right-power" your rig either. You should have both a speaker and amp that are way too massive for your current gig. :) But I digress.

Also, if your amp has a built in limiter that works properly and is turned on, it is nearly impossible to blow speakers from underpowering them, because the output will not clip. Of course, you can always generate a lot of distortion intentionally to overpower them, but that's difficult. And some amps are just plain defective (my Ampeg).

I regularly run 300W solid state into my cab rated at 800W. Sometimes biamped with a second cab rated around 700. It works fine, and I'm not pushing the speakers to their max excursion, so it sounds clean. (Of course, if you *want* that max-excursion sound, you have a whole different problem...)
 
Those that say underpowering is a myth simply do not understand the phenomenon. A clipped signal has more heating capacity than an unclipped signal. It is very unlikely that your 250 watt amp will approach the 750 watt limit clipped or unclipped. Thus, no problem.

For those of you that say its a myth, here is the scenario: You are running a 250w system when you need a 500w system. Your system is maxed out but you push it harder. Clipping the signal causing voice coils to over heat. The phenomenon is simply mis labeled, it is really "to much power can damage speakers". Where did the extra power come from? A clipped signal (square wave) has a lot more heating capacity (50% more) than an unclipped signal (sine wave).

You don't have to bellieve me. Go to electronics school and learn some ohms law. Anyone here ever heard of RMS (root mean squared).

Extremely unlikely anyone here will experience this but the theory is there, the potential is there.

"Underpowering" is indeed a myth. You're misunderstanding both clipping and Ohm's Law.

An amp will indeed put out more power when it clips than when it's right at the threshold of clipping (the point at which its output would be measured for its power rating). In fact, up to twice as much power, in the very unlikely event that the signal becomes a true square wave. A more powerful amp, though, would put out even more power than the clipping amp does if it were tasked with reproducing the same signal.
 
Clipping per se is not a problem, as the discussions in the sticky make clear. (1) Overpowering and (2) overexcursion are the potential problems. Those things can happen with a clipping amp, but also with a nonclipping one; hence, clipping per se is not the issue.

+1

You have said it clearly and succinctly, Richard. Thanks!
 
OK, but it's important to point out that the problem is really the overpowering. If you don't, people get the idea that merely connecting an amp capable of output X to a cab whose power handling is X + Y immediately creates an inherently dangerous situation. Which is nonsense and creates needless worry. I've seen this many times, and in fact the OP seems almost to be leaning that way, depending on the amount of credence he's willing to give those mysterious online sources.

The other misunderstanding that occurs is that, since when you push an amp past its clean limits it clips, the clipped signal per se is the culprit. But any bassist who uses a BIg Muff or similar device can tell you that their rig does not explode just because it's reproducing a heavily clipped signal.
 
That depends on what your definition of "underpower" is. You absolutely can not damage a speaker with too little power. You can send too much power, with an "underpowered" amp.

When tweeters, in a passively crossed system blow, it's not because the signal is clipped, it's because, in the high frequencies the tweeter sees, the signal ISN'T clipped (much). The bass may be 80% of the power, push the amp too hard, the bass clips first, so you end up cranking just the highs – bye bye tweeter.

Clipping is irrelevant. It just happens to be present, when underpowered amps, are over powering speakers. The problem is the over power, not the clipping.

I suspect that most of the risk of using an underpowered amp, comes from user error. The foolish, ignorant, muso assumes safety, and blissfully cranks it up.

Honestly, I don't know if I could tell the sound of an overstressed amp, from that of an overstressed speaker. At least with a too powerful amp, if something sounds bad, it's likely to be the speaker, so you turn down. Though it could be any gear in the signal chain pushed too hard. Not bass related but...I was running my wee PA at a house party, it started to sound horrible, I ran around checking for blown speakers. It turned out that the DJ had pushed his affordable mixer deep in to the red, it's weak pre-amps clipping like mad. Sounded like hell; didn't harm my speakers.
 
Those that say underpowering is a myth simply do not understand the phenomenon. A clipped signal has more heating capacity than an unclipped signal. It is very unlikely that your 250 watt amp will approach the 750 watt limit clipped or unclipped. Thus, no problem.

For those of you that say its a myth, here is the scenario: You are running a 250w system when you need a 500w system. Your system is maxed out but you push it harder. Clipping the signal causing voice coils to over heat. The phenomenon is simply mis labeled, it is really "to much power can damage speakers". Where did the extra power come from? A clipped signal (square wave) has a lot more heating capacity (50% more) than an unclipped signal (sine wave).

You don't have to bellieve me. Go to electronics school and learn some ohms law. Anyone here ever heard of RMS (root mean squared).

Extremely unlikely anyone here will experience this but the theory is there, the potential is there.

Alrighty then, I'll just take this 1/4 W headphone amp and my engineering degree and see if I can't blow up this 300W cab.

Perhaps my newly improved understanding of Ohm's law and it's practical applications will help me to do a better job on these 230,000V power lines I've been designing.

BRB
 
Well, maybe he was right . . .

I tried underpowering my cab to see what would happen. Sure enough, as I reduced power volume went down until, finally, the cabs stopped making any noise AT ALL. At this point, the head had been turned off but I am disturbed that neither the head nor the cab manufacturer saw fit to warn me abut this.

So let this serve as a warning to all TBers: operating your amp with 0 Watts will result in the COMPLETE FAILURE of your cabinets.
 
Well, maybe he was right . . .

I tried underpowering my cab to see what would happen. Sure enough, as I reduced power volume went down until, finally, the cabs stopped making any noise AT ALL. At this point, the head had been turned off but I am disturbed that neither the head nor the cab manufacturer saw fit to warn me abut this.

So let this serve as a warning to all TBers: operating your amp with 0 Watts will result in the COMPLETE FAILURE of your cabinets.

:D