Some of my trapped chests make no sounds at all when opened or closed. I have nine singles and six doubles. All of the singles and three of the six doubles are silent. In all cases, there are normal chests adjacent.
Three sets of three doubles stacked vertically like this make the expected noises:
CCTTCC
CCTTCC
CCTTCC
These trapped chests are all silent:
CCTCCTCCTCC
CCTCCTCCTCC
CCTCCTCCTCC
I also have a three high stack of doubles arranged in a 3/4 circle round a vertical pillar. They're silent too.
Vertical view:
Cdd
CdC
TTC
d - dirt, C - chest, T - trapped chest.
The only unusual thing I can think of is that I needed to shift-click to place these, because the normal chests were there first.
(See also MC-6019 which has the opposite problem - doubled sounds from chests.)
Confirmed.