Having a torn speaker cone can drastically lower the quality of sound coming from your stereo speakers. A small repairable tear in a speaker cone is usually only about an inch long and can easily be repaired with a few household items. If the tear in your speaker cone is longer than 1 inch, you probably should replace the damaged speaker cone with a new one.
Take the speaker apart and remove the cone. Stretch out the paper delicately and smooth it out as best as possible. One of the things that leads to a seriously damaged speaker cone is when the paper dries up, wrinkles and then tears, so smooth out the paper before beginning to repair the tear.
Pour some glue into a bowl and add some water. The best type of glue to use for this particular repair is Elmer's glue. The water you are adding is to dilute the glue. Don't use too much water since this could cause the mixture not to adhere and ruin the rest of the repair.
Cut a coffee filter into a patch that is 1/4 inch wider in all directions than the tear.
Flip the cone paper over and apply some of the glue water mixture to the back of the cone. Flip over the coffee filter patch and apply some glue to it as well.
Place the patch over the tear in the speaker cone. Use your paintbrush to work it into the paper and seal it properly. Give the cone at least a day or so to dry.
Reassemble your speaker and give it a test run to make sure the repair was successful.