160 Lecture 10 
Particularly in the special case of underwater acoustics with which I am 
concerned, the propagation of sound in shallow waters, full-scale methods are 
expensive, lengthy, and laborious; and, experimental sea conditions of common 
occurrence are not under ourcontrol, Thus, whenit is required to test a particu- 
lar aspect of the theory of sound propagation, it is rarely possible to find con- 
ditions at sea which enable the test to be made free from ambiguities. In practice, 
perturbing factors are often present which in one way or another mask the 
effect it is desired to detect. Theoretical treatment of propagation problems 
is also in many cases very difficult, and simplifying assumptions have to be 
made. Even skilled mathematicians, with the aidofmodern electronic computers 
and invoking idealized conditions, have hitherto found the answers to propagation 
problems in shallow water slow and tedious to obtain. Small-scale experiments, 
however, provide information much more rapidly and, evenif this information is 
not always as accurate quantitatively as we should like, it gives at least a reason- 
ably good guide to what we may expect to find under full-scale conditions. 
My interest in the subject of sound propagation in the sea was first aroused 
in 1915-16 when F.B. Young and I made some observations with an audio-fre- 
quency source (580 cps) of the sound field in water and around obstacles placed 
in the water [4]. During the course of our experiments, we noticed definite in- 
dications of a pattern in the sound field in the water, which we ascribed to the 
interference between the direct sound and that reflected from the surface and 
the bottom—somewhat similar to the Lloyd's mirror interference effect in the 
optical case, although more complicated due to the presence of the bottom. We 
also noted differences over soft mud and hard rock bottoms. It was not until a 
later date, 1934-35, however, that I had the opportunity for further study of the 
underwater interference problem. I then selected the relatively simple case of 
deep-sea propagation where there is only one surface reflection and no bottom 
reflection to consider. In this case it is easily shown that lines of maxima occur 
when the path difference S between the direct ray and the surface-reflected ray 
is an odd multiple of half a wavelength (n\/2). This indicates of course that the 
interference maxima can be represented by a family of hyperbolas, or, at ranges 
that are large compared with the depths of the transmitter and receiver, by the 
corresponding asymptotes of these hyperbolas. The experiments which I made 
at 300 kcps (wavelength, 5 mm) in a tank 80 ft long, 15 ft wide, and 10 ft deep, 
confirmed the simple interference theory, and in addition revealed temperature - 
gradient effects which caused bending of the lines of interference maxima. A 
receiver moving at constant depth d away fromthe transmitter at depth D passes 
through a series of maxima spaced at intervals increasing with range up to a 
critical distance 4Dd/\ where the path difference is equal to half a wavelength, 4/2, 
and beyond which the signal decreases steadily to zero at infinity. It was interest - 
ing to see these model experiments confirmed more recently in full-scale 
experiments by F.H. Sanders and R.W. Stewart [5,6] in very deep water off 
British Columbia. 
The main purpose of the experiments which I propose to describe is to 
examine the case of propagation of continuous sound waves in shallow water. 
Here we have to deal with the theoretically more difficult case which involves 
interference between the direct sound wave and waves reflected possibly many 
