Loudspeaker (6)
(Other definitions for woofer that I've seen before include "Loudspeaker to reproduce lower sounds" , "Loudspeaker that reproduces lower frequency sounds" , "Low-frequency speaker" , "Lab possibly" , "sound booster?" .)
'loudspeaker' is the definition.
(tannoy is a kind of loudspeaker)
This is the entire clue.
(Other definitions for tannoy that I've seen before include "Public address system" , "Speaker" , "Orator's amplifier" , "Loudspeaker system" , "Public-address system" .)