Physics + Math


How to Hear the Shape of a Room

Tim Wogan, writing for Physics World:

In his famous 1966 paper entitled “Can one hear the shape of a drum?” the Polish mathematician Mark Kac asked whether or not a listener could uniquely identify the shape of a vibrating membrane after hearing its resonant frequencies. In 1992 the American mathematician Carolyn Gordon and colleagues showed that the answer is no. In theory, however, it should be possible to hear the shape of a room by producing a sound and measuring the time taken for the echoes to arrive at particular points. But doing this in practice is not easy.

Now, though, researchers at the École Polytechnique Fédérale de Lausanne (EPFL) in Switzerland and Harvard University  have figured out how to do it, using a loudspeaker, four microphones, and an algorithm.

The algorithm that was created by the team only deals with first-order echoes, which means they exclude echoes of echoes. Lead researcher Ivan Dokmanić explains that this makes the system more practicable, as higher-order echoes can be too faint to isolate from background noise. However, isolating first-order echoes is also a challenge because it is not possible to say from a single recorded sound how many walls it has bounced off before reaching the microphone. The algorithm begins, therefore, by looking at the sounds recorded by the four microphones together and working out which sounds come from the same wall.

Grouping the echoes allows researchers to ascertain which were first-order and which were second. The arrival time of those first-order echoes, in turn, determines the size and shape of the room—information that could be valuable for the fields of architectural acoustics and audio forensics.