On the velocity of sound in water: theoretical aspects of Colladon's nineteenth century experiments

Abstract

In 1827, Colladon carried out a series of experiments in Lac Leman (Lake Geneva, Switzerland) to measure the speed of sound in water. The purpose of our contribution is to treat this measurement as an inverse problem, and show, by theory how to solve the latter. It is thus revealed under what circumstances it is legitimate to employ the time-of-flight scheme underlying the Colladon experiments and how to bypass this scheme in order to fully account for the temporal and geometric characteristics of the source (of sound), the temporal characteristics of the received signal and the error incurred by the finite distance between the source and receiver.