My Tannoy TS10 keeps blowing fuses and I get no power signal on the LED

The speakers consist of an induction coil, and a magnet attached to the cone. You have damaged something internally or the cone itself. Speakers don't have fuses unless they are powered speakers with mains input and an amplifier. You need the speaker repaired or replaced.

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https://www.tannoy.com/service.html

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Electrical issues are always a bit difficult to diagnose. Since I have not heard the wiring harness to be an issue on these, I would first look into if there was some add on causing an issue. Did you or someone add a trailer harness? Some type of additional lighting (like an LED bar)? Even possible a radio or under dash work? If not then do a once over and look at where the wiring comes through the firewall, or through the body to feed the turn signals. You just have to systematically follow the wiring from the lights back to the switch until you find the culprit. Let me know what you find and I can try to assist further.

If a fuse keeps on blowing there is a short in the wireing to that circut, Your best bet is to take it into a auto electric shop to be check out,

Judging by the rats nest of wires underneath your seat,...this may take some time to figure out. You have a direct short to ground on the power wire for the turn signals. Few questions......are you using led bulbs in the turn signals? Have you added a integrated taillight? Are you running anything else off of that circuit?..(neon lights,etc.) Have you checked the bulbs to make sure they are in correctly,and that the socket wires arent touching the inside of the socket?

The fuse is located under the AC input cable. Pull out the cable and you'll see there is a slot that will fitt a flat screwdriver. Pull this out and you'll find the fuse.

if you have a hum, then your fuse is ok.

Speakers don't cause a loud buzz but amplifiers do. Is it possible that the input to the amp lost it's ground? Regardless, this is not why the speaker does nothing but you would want to correct any amplifier problem before hooking up another speaker. If as you say, absolutely nothing happens it is possible that you blew out the voice coil of one of the drivers but blowing out both the woofer and tweeter simultaneously would be unusual, not to mention that Tannoys can take quite a bit of guff. So the next possibility is that there is a problem internally with the crossover or,and I doubt that it exists, and internal fuse associated with it. Since there is an LED (and I don't know what purpose it serves) there has to be some sort of power supply (fused?) to activate it. It could be derived from the audio output of the amp but it would then pulse on and off rather than just be constantly on. Getting inside the unit with an ohmmeter would quickly determine what's going on but I don't know how this can be meaningfully diagnosed at arms length and therefore just can give you some generic ideas.

sure. what do you want to know?
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Was not clear .....does the sub have audio output
If not the preamp circuit is bad and this will cause the hum as well

Have you checked the power supply. Maybe it has died.