But even this seemingly extensive list really includes only a few of the more obvious 

 parameters. Eq. (20) is presented, therefore, not as a complete statement of the form 

 of the relation involved but merely as an indication of its complexity. 



An experimental investigation of the sound produced by the vertical entry of 

 objects of just one shape and density (say, steel spheres) into water at ordinary condi- 

 tions would require the empirical determination of a function involving at least three 

 independent arguments. Moreover, even the most complete determinations might 

 describe the actual sound only stochastically, since the details of the motions which 

 result in sound are not necessarily reproducible. It is not surprising, therefore, that such 

 data do not exist. 



However, Franz [36] has shown experimentally that an important part of the 

 sound produced by the impingement of water droplets and small solid objects is 

 produced by the impact, so that only the density and compressibility of the water 

 are involved. The term "impact" here refers not merely to the sudden contact of the 

 surfaces but rather to the entire initial regime during the entry of a blunt or pointed 

 object in which inertial reactions predominate. Fig. 16 shows his experimentally 

 determined spectral distribution of the underwater sound energy radiated at the 

 vertical impingement of water droplets. The size and velocity of the droplets were 



10*' 





Figure I 6. 



to- 



la 2 



cr 



10' 



±jl 



$>•; 





«*a: 



• -2-- &-?.** 



• ••••, 



< J*n*Tt 



*h 



»• t* 







• • • 



E, Sound energy in ha f octave; 

 T =|-TTjOa 3 U 2 ; f, Frequency; 

 a, Radius of droplet (0.14 -0.35cm.); 

 U, Velocity of droplet at impact. 



10" 



10 



10 s 



la. 

 U 



Spectral distribution of underwater sound energy produced by the vertical impact of 

 water droplets. (Figs. 16, 17, and 18 from Franz [36].) 



varied over wide ranges. Nevertheless, the data define a single function when reduced 

 according to the analysis leading to eq. (19). It is not feasible to distinguish each 

 combination of droplet size and velocity in the plot, but the data show very little 

 systematic dependence upon either variable. Figure 17, traced from an oscillograph 

 record, shows the universal function describing the sound pressure. It will be observed 

 that the major part of the sound energy is generated immediately after the initial 

 contact and during an interval of time smaller than that required for the droplet to 

 travel a distance equal to its own radius. 



In addition to the sound of impact, droplets of certain combinations of size 

 and velocity occasionally produced a damped sinusoidal pulse of sound pressure similar 

 to that produced by the formation of an air bubble at a nozzle. The sound, when 

 it occurs, is caused by a tiny air bubble trapped beneath the surface by the splash. 

 Such a bubble is visible in the sequence of photographs in Fig. 18. This sequence is 



262 



