Sphinx, wow, cool. Never heard of it before. I don't have any experience wit it whatsoever, but when I googled it I noticed it was implemented in
Java, if not in other languages.
Therefore, your choices might be:
(1) Java
Applet, carrying the Sphinx packages, embedded within HTML page. A likely way to go.
(2) perhaps Flash somehow could embed it in an .swf file, but I don't know if Sphinx is compatible with Flash.