in 10,000. Applying the time -worn rule of thumb 

 which states that the hand-width required to pass 

 a pulse is the reciprocal of the rise time, it is 

 found that the bandwidth required in the system 

 is ^0 Mcps . From these assumptions the acoustic 

 delay is 127 x 10"° seconds giving an allowable 

 time error of 12-7 x 10"9 seconds and an allow- 

 able rise time of 25-^ x 10"9 seconds. This 

 requirement is so staggering that one instinc- 

 tively casts about for some way of reaching a 

 more reasonable answer. The rule used by oscil- 

 loscope manufacturers is less stringent and says 

 that the frequency band required is equal to 

 0.35 divided by the rise time between 10 and 90$ 

 amplitude. On this basis the bandwidth required 

 is only 20 Mcps or so. Perhaps this figure is 

 more practical. The main point here, however, 

 is to emphasize that a considerable bandwidth 

 is required if such a fast rise is necessary. 

 It should further be noted that a decrease in 

 path length, or in the allowable error, requires 

 proportionately greater bandwidth. 



There is a fundamental limitation which must 

 be evaluated hefore such a system is developed. 

 The attenuation in sea water is inversely pro- 

 portional to temperature. At 15 Mcps, for 

 example, the attenuation in the 7-6 inch path is 

 almost 10 db greater at 2°C than at 30°C, 

 while at 30 Mcps the difference in attenuation 

 between these temperature limits is over 30 db. 

 It follows that a pulse front containing energy 

 over a wide, high frequency range will be altered 

 in shape by this selective attenuation. 



From these considerations it seems unlikely 

 that freedom from systematic errors can be 

 achieved "by this means. Referring again to 

 Fig. 1, it can be observed that one way out of 

 this dilemma would be to compensate for the loop 

 gain of the system in some way. Since an 

 increase in loop gain causes a shortening of the 

 time interval and since an increase in the thresh- 

 old level causes a lengthening in the time inter- 

 val, it would seem that the threshold could he 

 controlled to produce an error compensating for 

 the gain changes which must he accommodated. It 

 can he observed that if the function reaches a 

 maximum in the same rise time, regardless of the 

 loop gain, then it reaches any given percentage 

 of its maximum in the same time. If then the 

 threshold is caused to change so as always to 

 equal some fixed percentage, say 50$, of the 

 maximum there would be no time error introduced 

 "by changes in the loop gain. Such a circuit 

 (compromising a simple peak rectifier) would per- 

 mit the use of rise times longer than would 

 otherwise be tolerable and consequently would 

 require less bandwidth. 



Other Pulse Characteristics 



Fig. 2 illustrates the type of pulse delivered 

 to the amplifier input from the acoustic circuit 

 in the Bureau of Standards type meter. The "Q" 

 of the transducers is so high that 5 cycles at 

 the resonant frequency occur hefore a maximum is 



Fig. 2. Standard acoustic circuit "behavior. 



reached. In practical use of the instrument a 

 loss in amplifier gain, an increase in acoustic 

 path attenuation, a mis-alignment of the trans- 

 ducers due to pressure effects, and/or a change 

 in the beam patterns of the transducers due to 

 frequency, pressure and temperature changes as 

 well as aging of the components, causes the sig- 

 nal to change in level. Under such conditions 

 the instrument will continue to function in appar- 

 ently normal fashion but will measure the time to 

 the wrong half -cycle. The resulting error with 

 the standard 3-6 Mcps crystals is about 270 nano- 

 seconds and produces an error in the indicated 

 sound speed of about 9 fps. This effect has been 

 observed on many occasions by various laboratories 

 and considerable effort has been expended in 

 critical readjustment and recalibration in order 

 to avoid this error. While it is possible to 

 prevent this shift by painstaking adjustment, 

 the fact remains that this is proof that the 

 errors discussed previously are in fact present. 

 It might further he observed that since the 

 velocimeter is normally calibrated by using dis- 

 tilled water at various temperatures, the error 

 is compounded in the actual calibration process. 



The pulse shape shown in Fig. 2 presents other 

 difficulties . Some of the energy arriving at the 

 receiving crystal is reflected back to the trans- 

 mitting crystal. Some of this reflected energy 

 is likewise reflected hack to the receiving crys- 

 tal. The difference in energy level between the 

 direct and the reflected energy is approximately 

 equal to the difference in attenuation (including 

 spreading losses) experienced by the 2 signals. 

 This value is approximately equal to twice the 

 loss in a single pass through the system. With 

 the type pulse shown, however, the signal from 

 the central portion of the pulse is much stronger 

 than the first or second pulses (either of which 

 may he used for the triggering pulse) and conse- 

 quently the reflected interfering signal is very 

 strong compared to the "signal" cycle of the 

 pulse. In addition, since these interfering 

 pulses occur very soon after the signal cycle and 

 since the electronic time delay is small, the 

 reflected pulse arrives at the receiver at essen- 

 tially the same time as the desired pulse causing 

 interference effects. 



158 



