Standing waves are involved in various fundamental, natural phenomena over a wide range of scales, that is, from electron orbitals to planetary oscillations. Interactions between standing waves and matter are of interest. Here we demonstrate spontaneous, nematodynamic standing waves in a nonlinear liquid crystal medium and their interactions with director fields. The standing waves hold unique features such as diagonal nodal lines, self-adaption to broad resonance frequencies and a step-like increase in the wavelength with the increasing frequency. Furthermore, the standing wave causes unexpected phenomena that can be used in various applications; for example, it can manipulate the molecular orientation to form tunable, periodic defect arrays with concentric director profiles, which can serve as an optical vortex array inducer or tunable micro-liquid crystal lens array. The standing wave also exerts asymmetric mechanical pressure that can relocate small particles. The results lead to new approaches in director manipulation, colloidal assembly and singular optics.