To check if you speaker is working correctly, first disconnect it from the amplifier by removing the wires from the speaker tag panel and then try these tests.
Gently move the cone in and out with your hand, the cone should move freely for a few milimetres before getting stiffer (do not force it or you could risk creasing the cone). There should not be any grating or scraping heard or felt. When released it should return to the equilibrium position in a ‘springy’ fashion.
Connect a battery across the terminals (we usually use a 4.5V radio battery). When the positive terminal of the battery is connected to the positive terminal of the speaker the cone should move away from the magnet assembly a small distance and stay there until the battery is disconnected.
Measure the DC resistance of the coil using a multimeter across the terminals. An 8ohm speaker should measure somewhere between 5 and 8ohm and a 16ohm around double that. If your readings are a lot different there may be a dry joint. Heat the tag with a soldering iron until the solder melts, then allow to cool. This will renew any dry joints. After a couple of minutes, you can re-measure.
Check the cone for tears or holes. These will lead to rapid failure, if they haven’t already. Small tears often cause buzzing and can be repaired with balsa cement. Use a small amount on the edges of the tear, and hold it together until it’s sunk in and stuck. Leave the speaker for a few hours before use.
However, not all audible problems are the speaker’s fault, buzzing is often caused by a cabinet panel or part of the amp that’s come loose. If you still have an audible buzz: press all the panels of the amp cabinet and chassis; ensure all the screws for amp and speaker are tight, and that no wires are resting on the back of the speaker cone.