Since you're looking for the offset of an exact match, the index function is ideal for you. There's no need to use an escaped regex (which could be done with /\Q$letter\E/).
Also, with a binary file, reading with the diamond op is chancy. You don't know where the audio may have a crlf pair. You clearly want to slurp the whole file into $word, so undefine $/ to make diamond do that.
my $word = do {
local $/;
<WORDSOUND>
};
my $offset = index $word, $letter;
If you need more sophisticated analysis, take a look at
PDL.
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