The frequency of vibration for arrays of this type can be approximated 

 by using the equation 



where 



f is frequency of vibration, 



N is Strouhal Number, 



V is velocity of fluid, and 



d is diameter of cable. 



Figure 12 shows the relationship of Strouhal Number and Reynolds Number and 

 can be used to compute the frequency for a series of speeds and cable diameters 

 It should be noted that these data refer to rigid cylindrical sections and should 

 be applied with caution to cables. Once an elastic body has been excited, the 

 motion of the body modifies the frequency. 



Figure 13 compares the frequencies measured on the system used in the 

 open-water tests with values computed by the foregoing method. It may be 

 seen that, in spite of the fact that the computed value is based on rigid cylinders, 

 it compares reasonably well with the low frequency components that were meas- 

 ured. The interfering components seemed to be composed of fundamental fre- 

 quencies and a number of related harmonics. These frequencies changed with 

 towing speed. The noise components were not present for the portion of the re- 

 cord taken when the boat was not moving. "When these components were present 

 on the record, they were of such a high level that the broad-band signal could 

 not be amplified to allow the identification of other signals without overloading 

 the analysis instrumentation. 



The results of the evaluation tests at sea are shown in Figures 14a and 14b, 

 the corresponding theoretical computations are superimposed for comparison. 

 It may be seen that, in these two cases, the theory and experiment are in very 

 good agreement. The system without the weight (Figure !4a) was observed to 

 tow in a reasonably steady manner. 



A qualitative frequency analysis of samples of hydrophone signals for th: - e 

 towing speed conditions was made. The records showed that there was con- 

 siderable interference due to cable vibration m the low frequency region at all 

 speeds. The frequency of vibration in these cases is proportional to the flow 

 velocity divided by the diameter of the cable. This was substantiated by the 

 records which showed that the frequencies received by the same hydrophone 

 became higher both with increased towing speeds for fixed diameter, and with 

 decreased cable diameter for fixed speed. The signals from hydrophones on 

 the weighted leg were higher in amplitude than those from the non-weighted leg. 

 This was attributed to the fact that the weighted leg was a better carrier for 

 the flow-induced vibrations than was the non-weighted leg. 



14 



