acoustically

The story

1. Proto-Indo-European*h₂eḱ-
2. Proto-Indo-European*h₂ew-
3. Proto-Indo-European*h₂ṓws
4. Proto-Indo-European*h₂ḱh₂owsyéti
5. Proto-Hellenic*akóuhō
6. Ancient Greekἀκούω (akoúō)
7. Ancient Greekᾰ̓κουστῐκός (ăkoustĭkós)
8. Medieval Latinacousticus
9. Englishacoustic
10. Proto-Indo-European*h₂el-
11. Proto-Indo-European*h₂élisder.?
12. Proto-Indo-European*leyg-
13. Proto-Germanic*līką
14. Englishacoustic
15. Englishacoustical
16. English todayacoustically

From acoustic + -ally, or from acoustical + -ly.