Abstract
A very interesting acoustical phenomenon, which we call sweeping echoes in a two-dimensional (2D) space, is described and investigated. Sweeping echoes in a three-dimensional (3D) space have recently been reported. In this paper, the regularity of reflected sound in a 2D regularly shaped space is first investigated based on number theory. The reflected pulse sound train has almost equal intervals between pulses on the squared-time axis as in a 3D space. This regularity of arrival times of the reflected pulse sounds generates sweeping echoes whose frequency increases linearly with time. Computer simulation of room acoustics shows good agreement with the theoretical results. In a practical situation, sweeping echoes were observed in a long hallway having a square section.
