bioacoustician

The story

1. Proto-Indo-European*gʷeyh₃-
2. Ancient Greekβῐ́ος (bĭ́os)
3. Ancient Greekβῐο- (bĭo-)
4. Englishbio-
5. Proto-Indo-European*h₂eḱ-
6. Proto-Indo-European*h₂ew-
7. Proto-Indo-European*h₂ṓws
8. Proto-Indo-European*h₂ḱh₂owsyéti
9. Proto-Hellenic*akóuhō
10. Ancient Greekἀκούω (akoúō)
11. Ancient Greekᾰ̓κουστῐκός (ăkoustĭkós)
12. Medieval Latinacousticus
13. Englishacoustic
14. Englishacoustician
15. Englishbio-
16. Englishacoustic
17. Englishbioacoustic
18. English todaybioacoustician

From either bio- + acoustician or bioacoustic(s) + -ian.