Infant vocalizations and "looming sounds" are classes of environmental stimuli that are critically important to survival but can have dramatically different emotional valences. Here, we simultaneously presented listeners with a stationary infant vocalization and a 3D virtual looming tone for which listeners made auditory time-to-arrival judgments. Negatively valenced infant cries produced more cautious (anticipatory) estimates of auditory arrival time of the tone over a no-vocalization control. Positively valenced laughs had the opposite effect, and across all conditions, men showed smaller anticipatory biases than women. In Experiment 2, vocalization-matched vocoded noise stimuli did not influence concurrent auditory time-to-arrival estimates compared with a control condition. In Experiment 3, listeners estimated the egocentric distance of a looming tone that stopped before arriving. For distant stopping points, women estimated the stopping point as closer when the tone was presented with an infant cry than when it was presented with a laugh. For near stopping points, women showed no differential effect of vocalization type. Men did not show differential effects of vocalization type at either distance. Our results support the idea that both the sex of the listener and the emotional valence of infant vocalizations can influence auditory motion perception and can modulate motor responses to other behaviorally relevant environmental sounds. We also find support for previous work that shows sex differences in emotion processing are diminished under conditions of higher stress.