there are plenty of articles on the internet dispelling egg trays as an effective soundproofing material.
hindi ko na gagatungan pa. at the risk of hastily generalizating, allow me to reduce soundproofing to three basic principles:
1) mass - the more mass the better; generally, anyway, because there are exceptions;
2) air tightness - where air goes, sound goes;
3) physical isolation - which explains why many designs call for floating rooms, room-within-rooms, etc.
if you want to go cheap, look for the most effective alternatives in these areas. good luck!