Well, i just did a search at hyundai-forums.com
I was trying to find the thread about a guy with an 02 Sonata which had approx 58K miles & 50 months on it when the timing belt broke & caused major engine damage.
Hyundai dealer said sorry but you did’nt change the belt according to the schedule in your owners manual, therefore-& rightfully so- the repair was NOT covered by the 60K warranty.
I could’nt find that thread?
If you look in your owners manual the change interval is every 60K miles or 4 years, whichever comes first.
Whether you have the 2.4 liter or the 2.7 liter engine they are both interference engines. Meaning bad things happen when the belt breaks.
Get the belt changed ASAP.
Do a search on “broken timing belt” at http://www.hyundai-forums.com you should find some interesting threads on this.