I can hear a difference between the pronunciation of the /ɔ/ sound in words like "audio" and "law." In the former, the vowel in question sounds more like the /ä/ in "car" (other words containing this same sound are "automobile" and "audience"), while in the latter, it sounds more like /ɵ/ (more like the vowel sound in "dog" or "raw").
My understanding is—and I might be wrong—that there are two different sounds involved in the pronunciation of the two aforementioned words, and that they are allophones of the phoneme /ɔ/ (at least in American English).
Could you please explain to me the difference between the /ɔ/ sound in words like "audio" and "law," and how to pronounce these two different sounds correctly in American English?