124 



USRL TEST STATIONS 



frequency and may be represented by the Fourier 

 integral: 



£(/) = / A, sin (Zvft- a 



f )df, 



(1) 



where A, and a, are the amplitude and phase of each 

 component frequency and E (/) gives the time varia- 

 tion of the resultant pulse amplitude and phase. For 

 most practical work only the dependence A f on fre- 

 quency need be determined. 



One method of obtaining this information about a 

 transient is to make a record of its wave form and ana- 

 lyze it. This technique may be used on high crest- 

 factor noises which cannot be analyzed with the usual 

 electric and recording systems. 



A schematic of the electric circuits for detecting 

 and recording transient wave forms of high peak pres- 

 sure is shown in Figure 62. A transducer is used to 

 convert the acoustic pressure to an equivalent voltage 

 which is amplified and impressed on a cathode-ray 

 oscilloscope producing a beam deflection propor- 

 tional at each instant to the acoustic pressure. By 

 photographing the oscilloscope screen on a motion- 

 picture film travelling at constant velocity, a record of 

 the transient wave form in amplitude and duration is 

 obtained. For accurate reproduction of the acoustic 

 transient, the phase distortion and frequency discrim- 

 ination must be kept to a minimum. 



A transducer with the XMX crystal head is selected 

 primarily because of its small size and uniform fre- 

 quency response. However, since this head has an 

 x-cut crystal of Rochelle salt, it is necessary that it be 

 terminated in an impedance much higher than its 

 own to minimize the effect of temperature. Because of 

 microphonic effects, it is necessary to place all elec- 

 tronic equipment a considerable distance away, pref- 

 erably out of the water entirely. This involves long 

 leads to the preamplifier. To prevent the hydrophone 

 from becoming temperature-dependent because of 

 the capacity of the connecting cable, a very small non- 

 microphonic capacity (C in Figure 62) is connected 

 in series with the crystal head at the junction of the 

 head and connecting cable. This is in effect a capaci- 

 tative voltage divider with an input impedance high 

 compared with the XMX head. As a divider it has 

 good phase and frequency characteristics as long as 

 any resistive components involved are high compared 

 with the shunt capacitative reactance. It is also to be 

 pointed out that any external capacity shunting the 



C s = TOTAL CABLE CAPACITY=I200/J^ 



INSERT CALIBRATING SIGNAL 



Figure 62. Schematic of circuit used in measuring 

 transients. 



cable capacity will further increase the voltage divi- 

 sion. The voltage-dividing effect of the network 

 serves a second essential purpose in reducing the 

 peak voltages resulting from high peak pressures to 

 the point where they are on the linear portion of the 

 preamplifier curve. The combination of crystal head, 

 voltage-dividing network, and cable is treated as a 

 unit and all acoustic calibrations are referred to the 

 end of the cable. 



The preamplifier serves also as an impedance trans- 

 former to provide a 100-megohm impedance to the 

 hydrophone and 72 ohms to the transmission line. 

 Two such preamplifiers are available, one with a gain 

 of — 1 1 db for high sensitivity heads, such as the XMX 

 type, and one with a gain of 35 db for low sensitivity 

 heads, such as tourmaline types. Both have a flat re- 

 sponse and a linear phase-frequency characteristic 

 from 2 c to over 600 kc. For almost all measurements 

 of transient phenomena, as well as those with high 

 peak pressures, this laboratory has used the XMX 

 head in conjunction with the first preamplifier. 



The oscilloscope used for these measurements is a 

 Dumont type 247 provided with an external supple- 

 mentary intensifier voltage for more brilliant traces. 



The records of the wave form were made on a mov- 

 ing film camera (Western Electric Fastax) with film 

 speeds up to 100 feet per second. Theoretically, fre- 

 quencies as high as 600 kc may be resolved at this 

 speed. The camera was used without the shutter 

 mechanism. With the moving film, no horizontal 

 sweep signal or transient sweep circuits are used in 

 the oscilloscope but the vertical amplifier which mul- 

 tiplies the voltage from the transient is essential. 



It is perhaps best to point out here that, while all 

 the electronic equipment was constructed with linear 

 phase-frequency characteristics over the entire range 

 of 2 c to 700 kc, the phase characteristics of the hydro- 

 phones are not entirely known. In general, if a hydro- 

 phone does not have any rising sensitivity with fre- 

 quency and if there are no "breakups" in the response 



