A. B. Wood 161 
times between surface and bottom. Some of the more important factors likely 
to influence sound propagation are contour, slope andnature of the sea bed, state 
of the sea surface, temperature and salinity gradients, water movements, and 
depth of water relative to the sound wavelength. The major cause of variation of 
signal strength in shallow water is, however, due to interference between the 
direct sound and that reflected from surface and bottom. The theoretical approach 
to the problem is very difficult even when this cause of variation is considered 
alone and all other variables are eliminated. The normal mode theory due to C. L. 
Pekeris [7] and various "ray" theories [7] have been developed to explain the 
main phenomena under idealized conditions. The present paper is concerned, how- 
ever, with a new experimental technique which gives a picture of the sound field 
under various prescribed conditions [9]. A brief reference is also made to a 
preliminary attempt by a mathematical computer method to reproduce such a 
sound field theoretically [8]. As was anticipated, the sound fields in shallow water 
are often very complex, but certain broad features depending on the ratio of 
depth to wavelength, the directional properties ofthe source, and the nature of the 
bottom are now apparent. 
10.1.1. The Scale of the Model Experiments 
The scale of the model experiments has been chosen somewhat arbitrarily 
and results from a compromise between full-scale requirements and available 
laboratory facilities. The shallow seas aroundthe British Isles vary considerably 
in depth but 100 to 200 ftisa reasonable average. The frequency range of present 
interest lies around 500 to 1000 cps, the corresponding wavelengths in sea water 
being about 10 to 5 ft (or 3 to 1.5 m). Considerations of this nature have led toa 
choice of tank dimensions 20 ft long, 5 ft wide, and 6 in. deep, approximately 
equivalent at full scale to 4 miles by 1 mile by 500 ft and representing a scale 
factor of the order of 1/1000. Usingthe same medium, water, on the model as on 
the full scale, we regard C=\N=A/T as constant. This is achieved by scaling 
down both wavelength » and periodictime T,or simply by increasing frequencies 
N by 1000/1. Consequently the frequencies 500 kcps and 1 Mcps, wavelengths 3 
and 1.5 mm, on the model correspond to full-scale conditions when water, in 
which C =1500 m/sec, is the medium employed. The mean ratio of depth to wave- 
length would under these conditions be around 20/1 in both full scale and model, 
the depth of water corresponding to a sea depth of 200 ft, being about 2 in. in the 
model. During the course of the experiments, however, the depth-to-wavelength 
ratio has been varied over the range from 30/1 to 4/1. 
The effects of loss of sound intensity due to attenuation or to increasing 
range have either been neglected or automatically compensated (reference is 
made to this later). 
The scale-model tank referred to above was made of sheet steel Y, in. thick 
suitably mounted and leveled ontables and fitted with side rails of Dexion girders 
on which a motor-driven platform carrying one of the transducers could move 
smoothly and quietly along the tank, as shown in Figs. 10.1 and 10.2. Provision 
was also made for driving the transducers across the tank and for raising and 
lowering them at any desired constant speed. In subsequent developments, to 
which I shall refer later, arrangements were made for raising and lowering 
a transducer at a controlled repetition rate (say, up and down three times per 
