problem with passing variables

I'm not sure if this is the right list for this, so bear with me.  If it 
isn't I'll be glad to post it on the correct one.

I've got a problem with passing variables to a SQL server inside a CGI 
script.  My code is like this:

my $begin_time = "2011-11-16 11:00:00";
my $end_time = "2011-11-16 12:00:00";

my $dbh = DBI->connect('dbi:mysql:database=embdev', 'user', 'password');

my $sql = q/SELECT * FROM events WHERE date BETWEEN $begin_time and 
$end_time/;

my $sth = $dbh->prepare($sql);
$sth->execute();

I'm not sure why it's not using the the variables, can someone point out 
what I'm doing wrong?

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Mark Haney