P. M. Kendig 251 
and this is simply the product of the total series resistance and the efficiency. 
This would be true even if the purely mechanical losses were not neglected. 
Therefore, substituting this expression for R;7 in Eq. (9) and making use of 
Eqs. (8) through (7), the free-field voltage response becomes 
ae o)k2 
Mo=\ 5 (18) 
The three quantities, 7, Mo, and P,, have also been obtained for two other 
shapes of piezoelectric transducers: a hollow, thin-walled cylinder loaded 
radially and a flat, circular disk radiating from both flat circular faces. For 
these cases, the radiation resistance per unit area was assumed to be the same 
as that of a sphere having the same radiating area. Further, the length / and the 
diameter 2a of the cylinder were assumed to be roughly the same order of 
magnitude. The results are given in Table 13.1. 
REFERENCES 
1, R.H. Mellen, "The Thermal-Noise Limit in the Detection of Underwater Acoustic Signals,” J. Acoust. 
Soc. Am., Vol. 24, 478-480 (1952). 
2. V.O. Knudsen et al., "Ambient Noise,” from Report No. 3, Survey of Underwater Sound (OSRD Report 
4333, NDRC Report 6.1-1848), PB 31021 (September 26, 1944). 
3. M. Lomask and R. Frassetto, "Acoustic Measurements in Deep Water Using the Bathyscaphe,” J. Acoust. 
Soc. Am., Vol. 32, 1028-1033 (1960). 
4, G.M. Wenz, "Some Periodic Variations in Low-Frequency Acoustic Ambient Noise Levels in the Ocean,” 
J. Acoust. Soc. Am., Vol. 33, 64-74 (1961). 
5. M. D.-Fish, "Marine Mammals of the Pacific with Particular Reference to the Production of Underwater 
Sounds,” Woods Hole Oceanographic Institution, Report 49-30 (1949). 
6. M.D. Fish, "An Outline of Sounds Produced by Fishes in Atlantic Coastal Waters,” Narragansett Marine 
Laboratory, Special Report No. 1, 53-1 (January, 1953). 
7. C.A. Teer, "The Influence of Hydrophone Directivity upon the Measured Value of the Ambient Noise 
Level in the Ocean," Underwater Detection Establishment, England, Report 65 (May, 1949). 
8. T. E. Heindsmann, R.H. Smith, and A.D. Arneson, "Effect of Rain upon Underwater Noise Levels,” J. 
Acoust. Soc. Am., Vol. 27, 378-379 (1955). 
9, R. J. Urick, "Some Directional Properties of Deep Sea Ambient Noise,” U.S. Naval Research Labora- 
tory Report 3796 (January, 1951). 
10. B. A. Becken, "The Directional Distribution of Ambient Noise inthe Ocean,” Univ. of California, Marine 
Physical Laboratory of the Scripps Institution of Oceanography, S10 Reference 61-4 (March 7, 1961). 
11. V.C. Anderson, “Arrays for the Investigation of Ambient Noise in the Ocean," J. Acoust. Soc. Am., 
Vol. 30, 470-477 (1958). 
12. V.C. Anderson, "Digital Array Phasing,” J. Acoust. Soc. Am., Vol. 32, 867-870 (1960). 
13. P.M. Kendig, "Factors that Determine the Equivalent Noise Pressure, Free-Field Voltage Response, 
and Efficiency of a Transducer at Low Frequencies," J. Acoust. Soc. Am., Vol. 33, 674-676 (1961). 
14. J.B. Johnson and F.B. Llewellyn, "Limits to Amplification,” Bell System Techn. J., Vol. 14, 85-96 
(1935), 
DISCUSSION 
DR. F.T. DIETZ, by way of augmenting the lecturer's remarks, mentioned 
the results of ambient noise studies being carried out at the University of 
Rhode Island in a shallow-water location. The main objective in the systematic 
measurements made was to find any possible seasonal variations and to deduce 
any possible correlations between the ambient noise spectrum and environmental 
parameters, such as wind speed and direction, tidal currents, etc. 
Some 864 spectrum determinations were made on a ‘'/-octave basis in the 
range 40 cps to 10 ke using a "bottomed" hydrophone in a water depth of ap- 
proximately 30 ft. The results revealed that after a critical value of the wind 
speed is exceeded, then the acoustic pressure levels are linearly related to the 
