How long does it take a loose tooth caused by trauma to tighten?

Depends. Injured teeth may seem loose because they're cracked (split into 2pieces) and often require extraction. If your dds said the tooth is intact, then soft diet and possibly having your dentist temporarily splint (attach the loose tooth to neighboring tight teeth) can aid in the tightening of your tooth. Time is variable from a few weeks to several months.
Depends. I placed a patient on a nutritional program and his tooth tightened up in a few days! other patients have lost teeth its going to depend upon how severe the trauma wasand, how healthy your system is..... You might start taking the homeopathic remedy traumeel. Get this at a health food store get the liquid and take 6 drops 5 time a day for the next few days.