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

TL;DR

This paper analyzes Colladon's 19th-century experiments measuring sound speed in water, framing it as an inverse problem and providing theoretical insights into the measurement's validity and potential improvements.

Contribution

It introduces a theoretical framework for solving inverse problems related to sound speed measurement, clarifying conditions for the time-of-flight method and accounting for source and receiver characteristics.

Findings

Identifies when the time-of-flight scheme is valid

Provides methods to account for source and receiver temporal characteristics

Analyzes errors due to finite source-receiver distance

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.