The orthogonal axes chosen for the transverse waves is chosen because of the asymmetric coupling in the two directions. On a flat-top acoustic guitar the top plate moves up and down "more easily" then from side to side.
Fragment of CONTRACTIONS, mobile for woodwind quintet 1965. Each of the 5 players follows a concentric circle in either direction. Graphic notation alternates with traditional notation. Originally published by E.C. Schirmer, Boston. Copyright transfered to Richard Felciano in 2003. By permission.