Conventional distance sampling, the most-used method of estimating animal density and abundance, requires ranges to detected individuals, which are not easily measured for vocalizations. However, in some circumstances the sequential pattern of detection of vocalizations along a transect line gives information about the range of detection. Thus, from a one-dimensional acoustic point-transect survey (i.e., records of vocalizations detected or not detected at regularly spaced listening stations) it is possible to obtain a useful estimate of density or abundance. I developed equations for estimation of density for one-dimensional surveys. Using simulations I found that for the method to have little bias when both range of detection and rate of vocalization need to be estimated, stations needed to be spaced at 30–80% of the range of detection and the rate of vocalization should be >0.7. If either the range of detection or rate of vocalization is known, conditions are relaxed, and when both parameters are known the method works well almost universally. In favorable conditions for one-dimensional methods, estimated abundances have overall errors not much larger than those from conventional line-transect distance sampling. The methods appeared useful when applied to real acoustic data from whale surveys. The techniques may also be useful in surveys with nonacoustic detection of animals.