Visual perception of longitudinal waves: theory and observations

We introduce the study of the visual perception of longitudinal travelling wave motion, which as a physical phenomenon forms the basis of acoustics and some forms of seismic transmission. A theoretical analysis of physical longitudinal wave motion reveals that it exhibits profound nonlinearities that have been almost entirely neglected by the physics community. We simulated longitudinal motion in visual form with a random-dot field in which each dot particle oscillates sinusoidally about a fixed position at the same frequency but with a phase advance proportional to its distance from the origin. The resultant longitudinal density wave is essentially sinusoidal at very low oscillation amplitudes, becoming progressively distorted as oscillation amplitude increases. Perceptually, the motion splits into a combination of forward motion of the crests and backward for the troughs, rather than a uniform travelling wave. When the maximum velocity of each dot particle equals that of the propagation, the density function approximates a narrow spike, which splits into a double spike at even greater amplitudes. Adding a single ('rigid') velocity component can eliminate either the forward or backward percept. Remarkably, the speed needed for perceptual cancellation scales with oscillation amplitude, but nonlinearly so for the forward crest motion. Longitudinal waves evoked no motion aftereffect at any amplitude unless the contrast of the forward crest motion was reduced, revealing a motion aftereffect from the now-dominant retrograde trough motion. These unexpected results underline the emergent, or higher-order, nature of the perception of longitudinal travelling wave motion.