244 Lecture 13 
13.2. THE MEASUREMENT CF AMBIENT NOISE 
We have seen that at high frequencies the ambient noise is dominated by 
thermal noise and represents the lowest detectable signal possible with an 
omnidirectional hydrophone of 100% efficiency. However, at lower frequencies 
(below about 40 kc), the sea ambient due to other causes and that due to thermal 
noise diverge about 11 or 12 db/octave as the frequency is reduced. Thus, it 
should become increasingly easy to measure the sea ambient as the frequency 
is reduced below 40 kc. However, there are other factors which tend to counter 
this advantage. The principal one is the reduction in the acoustic loading on the 
hydrophone for those cases where the wavelength is much greater than the di- 
mensions of the hydrophone. Since this loading varies as the square of the fre- 
quency in the low frequency range, itis quite incapable of measuring the thermal 
noise. But with proper attention paid to allthe design parameters, the equivalent 
noise pressure may be kept well below the sea-surface ambient in the low 
frequency region. 
The equivalent noise pressure of a hydrophone is that acoustic pressure due 
to plane sound waves which would produce the same open-circuit voltage across 
the terminals of the hydrophone as is produced by the thermal noise of the 
hydrophone in a 1-cps band. 
A hydrophone for broad-band underwater sound measurements should be 
essentially omnidirectional and have a flat, free-field voltage response over 
the frequency range. Section 13.3 indicates those factors which determine the 
equivalent noise pressure ofa linear hydrophone that obeys the reciprocity re- 
lation, that is small compared with the operating wavelength, and that operates 
in a frequency range well below that which would permit any self-resonances. 
These are the characteristics required for omnidirectionality and flat response, 
and are quite easily attained with several shapes of piezoelectric transducer 
elements—especially those made of electrostrictive ceramic materials. Three 
shapes will be considered: a hollow spherical shell, a hollow circular cylinder 
loaded on the cylindrical surface, and a flat circular disk loaded on both cir- 
cular surfaces. A number of approximations were made to better exhibit the 
Significance of each of the parameters. Details of the development are given 
only for the spherical shell, but the results are given for all three in Table 13.1. 
The results shown in Table 13.I do not include mechanical losses; but in a 
well-designed transducer these losses should have negligible effect at these low 
frequencies, which are well below all hydrophone resonances. 
The expressions for the efficiency show that it is strongly dependent upon 
the frequency and physical size of the transducer. For any present piezoelectric 
ceramic transducer, the second term in the denominator is small compared 
with the first. Thus, the efficiency is, approximately, in direct proportion to 
the square of the electromechanical coupling coefficient and inversely propor- 
tional to the loss tangent. Note that 1~—k2 does not differ greatly from unity, 
since k2 is always less than unity and is usually fairly small. However—and 
this is significant—if the coupling coefficient approaches unity, or if the loss 
tangent approaches zero, the efficiency approaches 100%. This demonstrates the 
important role played by each of these parameters. 
