234 | ANNUAL REPORT SMITHSONIAN INSTITUTION, 1944 
account the temperature and salinity differences. But where the 
depths in the area vary to a marked degree, and especially where the 
depths are too great to permit tests to be made, the velocity of sound 
values must be determined from an assumption of the path of the 
sound wave. 
There is also an indirect method for determining the effective hori- 
zontal velocity of sound under certain conditions and allowing certain 
assumptions. If the time intervals from a bomb explosion to three 
receiving stations at known positions are measured accurately, and 
the same temperature and salinity conditions and depths along the 
three paths of sound are assumed, then the effective horizontal velocity 
can be computed by means of a rather involved formula. It is obvious 
that there must be no doubt regarding the accuracy of the travel times. 
If one value is doubtful or if the conditions along the three paths are 
dissimilar, an erroneous value of the velocity of sound will result. 
PATH OF A SOUND WAVE 
In an ideal water medium with uniform characteristics and unlim- 
ited dimensions in every direction, a sound from a nondirectional 
source would be propagated along straight paths in every direction. 
The arrival time at any receiving station would be the time required 
for the sound to travel the shortest path. In such a case, the theoreti- 
cal velocity of sound would be the same as the effective velocity, and 
R. A. R. would not be complicated by uncertainties due to the path of 
the sound wave. 
Unfortunately, the ideal medium does not exist in practice, and the 
propagation of sound in water is indeed complicated. The sound wave 
is propagated through a body of water bounded above by the water 
surface and below by the ocean bottom; the horizontal dimension of 
the medium is long as compared with its vertical dimension; sound 
waves are reflected from both boundaries of the medium, and within 
the medium they are refracted by changes in the velocity of sound 
along the path. These facts complicate the path of the sound wave. 
The reception of sound is also complicated by the fact that the vari- 
ous reflected and refracted waves interfere with one another. Where 
two sound waves of the same frequency and wave form meet at one 
point, they will tend to reinforce or neutralize each other, depending 
on their directions of propagation and whether they meet in the same 
or opposite phases. 
It is apparent that, in a bounded water medium, the sound wave 
may travel an almost unlimited number of paths. There will be one 
direct path from the source to the receiver and a multitude of reflected 
paths. The sound wave that first arrives at the receiver with sufficient 
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