It is very easy to puncture a speaker cone. When this happens, the drive unit can buzz or crackle when sounds are being reproduced. It is a most unpleasant sound.
The buzz or grating sound is caused by the small fragments of cone around the hole vibrating. A further issue is that if the speaker is used with an enclosure, the hole will cause loss of pressure and cause the backward wave to emanate from the front causing cancellation. This will change the sound from the overall speaker system. When this happens the speaker needs replacing or repairing.
Speaker cone repair
Sometimes it can be possible to obtain and fit replacement cones. If no other method is available one last ditch method to save and repair the loudspeaker that has worked well in the past uses a small patch.
Most speaker cones are made of paper, and so a repair using some tissue paper works well. It may also be suitable for other materials, but assess the break and material to find a suitable alternative if necessary.
Take the tissue paper and cut it so that it covers the hole, with a small overlap around the hole. The tissue paper is sufficiently light that it should not affect the operation of the speaker unduly.
It may be worth testing the tissue paper and the glue together first to make sure that the tissue paper does not shrink - this could distort the cone.
This tissue paper can be glued to patch the hole. Make sure all the tissue paper has glue and that there are no lose edges otherwise these could create a buzz. If possible repeat the process on the under-side of the cone if it is accessible so that the repair is secured from both sides.
Use a flexible glue and then the rigidity of the cone will not be affected too much. Also use the minimum glue consistent with creating a firm bond, otherwise the mass of the cone will be altered and its performance changed.
Leave the loudspeaker until all is dry and the test it out.