Taken from http://billfitzmaurice.info/forum/viewtopic.php?t=1886

This excellent treatise explains why underpowering is a myth, one that unfortunately refuses to die:

Amplifier clipping, and it's respective causes and effects, is perhaps one of the most misunderstood concepts amongst audio circles. There is a whirlwind of myths surrounding this topic that seems to exceed all other topics I have come across. Now is your chance to learn the truth about clipping.

How Do Speakers Become Damaged

There are only two ways that a speaker can be damaged, both of which occur from too much input power. 1. Mechanically 2. Thermally

Every speaker has an excursion limit (often measured in mm), or how far the speaker can move forward or rearward before damage occurs. This is the mechanical limit of the speaker. This limit remains the same regardless of the use of the speaker, but the power required to reach this limit changes dependent on the enclosure. If you exceed this limit, the speaker will suffer mechanical damage, whether it's ripping your spider, bottoming out on the back plate, or any other mechanical damage. The second type, thermal damage, occurs when you exceed the thermal power handling limits of the voice coil itself. Voice coils are simple pieces of metal that will melt if too much power is applied. This limit is pretty much constant, ie. if a voice coil will be damaged at 1 kw, it will be damaged at 1kw regardless. There are two final myths to cover here. Despite the tireless efforts of some, there are still many people that believe that underpowering a speaker will damage it or that clipping will damage a speaker. Please remember that these last two thoughts are entirely UNTRUE! And now we will find out why.

Where Does This Power Come From?

Let's first understand the power potential of an amplifier when clipping. The power created is largely determined by the rail voltages. Let's compare two amps, each one connected to a 4 ohm speaker rated at 75 watts rms. Amp 1: 50 watt amp 50 Watt amp means this amp can cleanly deliver a sinewave of 50watts into a 4 ohm load. This means (Vrms)^2/4 = 50W Vrms = 14.14V Vpeak = Vrms*(1.414) Vpeak = 19.99V The rail voltages of this amp must be a bit higher, to prevent output stage distortion at this power level. In this case, the Rail voltage would have to be +/- 20 Volts. Amp 2: 75 watt amp (Vrms)^2/4 = 75W Vrms = 17.32V Vpeak = Vrms*(1.414) Vpeak = 24.49V In the example, the 75 watt amp is delivering 75 watts as it is not distorting at all. The 50 watt amp is in hard clipping, as and such, is delivering a fair bit more power. P = Vrms^2/R = (19.99V)^2/4 ohm = 100 watts. It is quite obvious that there is potential for an amplifier that is clipping to deliver substantially more power than you would expect. Keep in mind that this is only a way to determine peak voltage potential.

Average Power

Now we can get into how a speaker really gets hurt. The key issue is average power over time. Let's get to the nitty gritty. The first key is understanding Crest Factor.

"Crest Factor" is the difference between the average level of the signal and its peak level. A pure sine wave has a "crest factor" of 3dB, meaning that it's peak level is 3dB higher than its average level. We all know that 3dB represents a difference in power by a factor of 2. Another way to look at it is that the peak power of the signal is twice that of its average level. If we were to play a sine wave on our 50 watt amplifier, just below its clipping level, the average power over time the speaker would need to dissipate is 25 watts. On the other hand, a square wave has a crest factor of 0dB. In other words, its average power and peak power levels are equal. Our same 50 watt amplifier playing a square wave into our speaker requires the speaker to dissipate 50 watts. Keep in mind that this refers to sine and square waves only. Music has a much higher crest factor. Most widely available recordings have a crest factor of approximately 10dB. Looking at this in terms of power, the peak power is 10 times greater than the average power. If we were to play one of these recordings with our 50 watt amplifier when not clipping, the speaker needs to dissipate a mere 5 watts of average power over time. When the amplifier begins clipping, the peak level/power does not increase. BUT, the average power DOES increase. If we were to turn the volume up 6dB higher than the clipping level of our recording, we have reduced our crest factor to 4dB. Guess what? We are now needing the speaker to dissipate 20watts. This is four times the average power and four times the heat when measured over time. As you can see here, it is not the distortion or the waveform or anything along those lines that is killing your speaker; there is simply more average power over time. However, if the average power of time is still below what your speaker can handle, it doesn't matter if it's clipping or not. At higher power levels, the fact that a clipped signal carries more average power over time can result in damage.

DC in Clipping

One of the most famous myths regarding clipping is that it produces DC. The assumption is made because of the flat tops and bottoms to a square wave. It's incorrect to think of a squarewave as made up of positive and negative dc components. The only way for a it to be DC would be if there was a non-zero average value over long periods of time. If the polarity changes at all within the time frame that you are looking at, it is simply not DC. What are these flat portions of the signal? It is simply a combination of the fundamental frequency and all of it's higher order harmonics in sine wave form. For example, if you were to play a 20hz tone while clipping, there would be the fundamental frequency (ie. 20hz) and the second (40hz), third (80hz), and 4th (160hz) order harmonics. The sum of these frequencies creates what appears as a squarewave. There are two ways to test this for yourself; one is quite easy, the other is a little more advanced. The first way is simple if you have a variable crossover and an oscilloscope handy. Pass a low frequency square wave. You will notice the square shape on the oscilloscope. Now turn your crossover's low pass filter on. Slowly lower the setting as you approach the fundamental frequency. You will notice the waveform on your oscilloscope slowly rounding off into a typical sinewave. Once you have reached the fundamental frequency, your oscilloscope will show a perfect sinewave. The second way is for your math guys (or for those who like to use Matlab). If you look in the frequency domain using a Fast Fourier Transform, you will see the fundamental frequency and its higher order harmonics only. There will be absolutely no DC present.

Clipping and the still voice coil

The final myth is that of the still voice coil. It is perhaps the most believed myth regarding clipping. The idea is that because of the square wave, the coil is not moving during the flat portions of the signal. This is simply not true for a variety of reasons. The speaker does exhibit mechanical damping and remains in constant motion. Assuming the same voltage and excursion xmax, the cooling at any given frequency will remain the same, whether the signal is clipped or unclipped. Here is a great article to read on the cooling effects and how a driver fails under various waveforms:

Summary

To provide a final review of all that we have discussed on this topic, there are only two ways to damage a speaker: Mechanically and Thermally. The only way to do this is by applying too much input power in a given enclosure (mechanically) or too much average power over time (thermally). There is no DC in a clipped signal; the coil does not stand still; air passing over the coil (and thus cooling) is the same regardless of the waveform; and clipping is acceptable provided that the average power over time is lower than the speaker's limits. The next time you hear those famed words "your speakers died because of clipping", remember what you have learned, and above all, keep searching for the truth. It's out there somewhere.