Why are DC signals bad for loud speakers?

ALL current will heat the voice coil of a speaker. But AC current is useful to reproduce sounds (which is what a speaker is made for).

On the other hand, DC current will produce the equivalent amount of heating as an equivalent AC current, but it will produce nothing but a fixed offset (versus moving the cone in and out to produce sound). And while you can hear AC current, and you can hear when it is "too loud" and distorting the speaker, you cannot hear DC, so you don't know whether your speaker voice-coil is sitting there frying until you see the smoke.Also DC current biases the cone off center which could increase even harmonic distortion.

For these reasons it is never a good idea to allow DC current to go into a speaker voice-coil.

The voice coil on a speaker is effectively a big inductor. It happens to also generate sound, but the loops of wire in a magnetic field make it act like an inductor.

Inductors change impedance with respect to frequency. This is because any change in current through the system must build up the magnetic field in the coils. The faster you oscillate the current, the more pronounced the effect. This causes inductors to have a high impedance at higher frequencies, and a low impedance at low frequencies.

So what happens at DC? Well the impedance of an ideal inductor at DC is 0. That means no resistance at all! Of course, this isn't an ideal inductor. There is a bunch of wire, and that wire will provide some resistance. However, it is trivial to see that the resistance of the coil at DC will be far less than it will be at a higher frequency.

Now most amplifiers are voltage sources. They output a specified voltage, and are designed to provide enough current to maintain that voltage across the impedance of the speaker. Thus, if you have a very low resistance, you will have a very high current, much higher than might otherwise form. This current means your coil has to dissipate a lot of heat!

Sound consists of pressure changes in the air.

You can generate these pressure changes using a loudspeaker.

The loudspeaker generates these pressure changes (sound waves) by moving a diaphragm back and forth.

This diaphragm is moved back and forth by a voicecoil consisting of a "pipe" with some electrically conductive wire wound onto it.

This voicecoil is suspended in a magnetic field provided by a permenent magnet.

If you would use the loudspeaker properly and only apply an AC signal to it the voice coil would move some distance to the front and the same distance to the back. This is because the average of the signal you're applying is 0 (zero), the signal has a DC value of zero. On average (over a some time) the position of the voice coil is at it's center point, the "resting" position, the same position it would have if you applied no signals to the loudspeaker.

Now if you would apply a DC signal there would be a constant force working on the voice coil constantly moving it a little bit to the front or (if you reverse the polarity) a little bit to the back. If you would also apply an AC signal the loudspeaker would still work but on average it would not be in it's center "resting"position.

This DC signal induces a constant force on the voice coil but it also heats it up as there is a current flowing and since the voicecoil's electrical wire has some resistance (4 or 8 ohms usually) some power will be dissipated heating up the voice coil.

Another side effect is that good loudspeakers are designed such that the voice coil can move a certain distance to the front and a similar distance to the back. If you apply a DC voltage then you offset this as the distance the voice coil can travel will be asymmetric. If the voice coil can move 10 mm to the front and 10 mm to the back but you offset it with a DC signal by 5 mm to the front, the voice coil can only move 5mm to the front and 15 mm to the back. This will result in more distortion and worse sound quality.