© 1954 by Oxford University Press
NOMOGRAMS FOR THE SOLUTION OF THE SOUND-RANGING PROBLEM IN A PLANE
( King's College Newcastle-upon-Tyne )
Nomograms are devised for locating a source of sound in the plane defined by three collinear receivers and the source, given the times of arrival of the sound at the receivers. This is formally equivalent to the construction of a circle to touch three given circles having collinear centres.
Though the time of emission of the sound is not usually of interest, its determination forms a useful intermediate stage in the calculations. Thus three unknowns must be determined, but it i shown that only two nomograms are required: the first giving the time of emission and one coordinate of the source by a single setting of the index-line, and the second giving the remaining coordinate.
The nomograms described possess special advantages when the solution is overdetermined by the use of data from more than three receivers, since each additional receiver may be dealt with by adding an additional scale to the first nomogram. The mean solution is then obtained by setting the index along the best straight line through the points denoted by the entry values of all the observed distance differences. The second nomogram is unaffected.