were made so carefully, that the sound peaks at the Strouhal number, which is usually 

 associated with the vortex street. This suggests some kind of regular pattern of vortices 

 associated with submerged jets, the value .18 or .2, suggests the vortex street. 



The purely hydrodynamic noise is, of course, hard to find, unless you go to 

 a submerged hydrodynamic oscillator in which there may be no free interfaces what- 

 soever. In this case one can generate pure hydrodynamic noise by exciting a resonant 

 system in relatively incompressible liquid. 



There are old cases of controversies of this type, about whether you should 

 streamline hydrophones, where people have said that there is no hydrodynamic noise 

 of significance, but experimental tests have shown some anomalies. For example, point- 

 ing directional hydrophones at submerged bumps on objects, one will get a noise coming 

 from this bump, under conditions in which cavitation really could not exist at all. 

 There is a real mystery there, and if one can throw some light on this subject, it would 

 be well worth while. 



There may be the question of compound interferences from roughness, and so 

 forth, putting the interface into the system somewhere, or tiny bubbles, but in the 

 absence of the interface, it is really hard to explain some of these noises. 



M. Strasberg 



Dr. Gongwer's comment about one of our spectrum curves indicates that the 

 curve requires some clarification. I believe he stated that our curve of the spectrum 

 of the radiated sound from a jet had a peak at a Strouhal number of about 0.2, sug- 

 gesting that some regular vortex pattern might be associated with the jet. However, 

 on the curve referred to we did not use the Strouhal number, but rather a dimension- 

 less frequency based on the sound velocity. 



We use two types of dimensionless frequency. For the sound close to the jet, 

 where the behavior is the same as in an incompressible fluid, we do use the Strouhal 

 number, frequency times diameter divided by flow velocity, as the dimensionless fre- 

 quency parameter. On the other hand, for the sound radiated far from the jet, we 

 think it is more appropriate to use a dimensionless frequency based on the sound 

 velocity, that is, frequency times diameter divided by sound velocity. 



There is some question whether either frequency parameter by itself is adequate. 

 Actually, both parameters may influence the radiated sound. But we think that the 

 radiated sound depends more on the parameter fD/c than on fD/U . 



So it was just an accident that the peak occurred at a value of 0.2, the same 

 as the Strouhal number for vortex shedding. 



T. B. Benjamin 



I wish only to emphasize the importance of one aspect of underwater noise 

 touched upon in Strasberg and Fitzpatrick's excellent survey. This is the formation of 

 real shock waves, akin to underwater blast waves, by collapsing cavitation bubbles. 

 To call to mind this effect, it may be remembered that the pressure pulse produced at 

 a distance by a cavitation collapse can have an effective duration of about 10 micro- 

 seconds; but under some circumstances the pulse may develop a shock front whose 

 transit past a fixed station may occupy considerably less than one microsecond, that is, 

 very much less than that of the whole pressure wave. 



There appear to be two respects in which the presence of shocks may be 

 specially important, the first being their role in cavitation damage. In writings on this 

 subject the term "shock wave" is used extensively, and the importance of the brief 

 duration of cavitation pressures is fully appreciated; however, the distinction between 

 very short yet continuous pulses, such as would always occur if water were strictly 

 incompressible, and real shock waves is not always recognized. Nevertheless, one is 

 naturally led to give weight to this distinction, since it is known that the stresses devel- 

 oped in a solid boundary by the incidence of shock waves are much greater than those 

 due to continuous pressure pulses of the same amplitude. Some experiments done at 



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