Sounds exasperated by announced dimensions (5)
I believe the answer is:
sighs
'sounds exasperated' is the definition.
(someone who is exasperated might sigh)
'announced dimensions' is the wordplay.
'announced' indicates a 'sounds like' (homophone) clue.
'dimensions' becomes 'size' (I've seen this before).
'size' is a homophone of 'SIGHS'.
'by' is the link.
(Other definitions for sighs that I've seen before include "Sounds of weariness" , "Sounds despondent" , "Lamentations" , "Moans" , "Yearns" .)