30 



TYPES OF ACOUSTIC MEASUREMENTS 



unit and its preamplifier, a case which is discussed 

 below. 



The threshold pressure for low-impedance hydro- 

 phones may be computed from the receiving response 

 R R and the resistance of the hydrophone r. This rela- 

 tion is as follows: 



Substituting in the above equation (14) for e,„ the 

 value given by equation (11) leads to the results 



1.79 x 10- lo \/r. 



(17) 



The signal voltage is related to the signal pressure p 

 (in dynes per sq cm) by means of the receiving re- 

 sponse R R , in accordance with equation (10), 



R* 



20 log (J) 



which may be written in the form 



20 log p = 20\o S e g -R K . 



Introducing in this equation the signal voltage de- 

 fined by equation (17), we obtain the threshold pres- 

 sure in decibels 



T = 20 \ogp = 20 log (1.79 x lO-^x/r) - R n 



= 10 logr- 194.9 -R B . (18) 



The test procedure in accordance with the above is 

 to measure the resistance and response of the hydro- 

 phone. From these values the threshold pressure then 

 is computed by means of equation (18). 



Measured Threshold 



For a high-impedance hydrophone of the crystal 

 type, the active element is usually directly associated 

 with a preamplifier. This is necessary in order to 

 avoid excessive losses in the leads and also to pre- 

 vent noise pickup, to which a high-impedance circuit 

 is apt to be subject. Frequently the preamplifier is 

 given an extremely high input impedance. This is 

 done in order to obtain the maximum signal-to-noise 

 ratio at the first grid (as discussed) and also in order 

 to stabilize the hydrophone. For instance, in the case 

 of x-cut Rochelle salt crystals, which are inherently 

 variable with temperature, the variability is reduced 

 when no current is drawn from them. 



Since the preamplifier is so intimately associated 

 with the active element, it is best to treat the two as 

 one unit and to determine the threshold for the com- 

 bination. As a rule, the noise of the preamplifier ex- 

 ceeds the thermal noise to such an extent that the 

 latter has little practical importance. The computa- 

 tion outlined above then becomes useless and the 

 only practical way to proceed is actually to measure 

 the inherent noise level of the instrument. This re- 

 quires an extremely quiet body of water and a very 

 quiet measuring system in order that extraneous 

 noise does not enter into the tests. When quiet water 

 is not available, a possible alternative is to substitute 

 a network for the crystal. The latter must be the elec- 

 trical equivalent of the crystal in water over the entire 

 frequency range included in the measurement. The 

 measuring system, in addition, should have uniform 

 response and a definitely defined band width, narrow 

 enough so that variations in the hydrophone response 

 within the band may be neglected. Usually the pre- 

 amplifier output is matched. If the measuring band 

 includes the frequencies from ] x to / 2 , then the value 

 10 log (f-> — fi) must be subtracted from the measured 

 noise voltage (assuming it to be in decibels), in order 

 to obtain the threshold. 



4.3 



RELATIONS BETWEEN 

 MEASUREMENTS 



In the following, certain relations that exist be- 

 tween the measured quantities are pointed out. 59 

 These relations frequently are useful in cross-check- 

 ing measurements. They also reveal additional in- 

 formation as to the nature of the definitions. 



1. The relation between the projector efficiency 

 E p and the transmitting response R T was given 

 in equation (8): 



E p = R T + A- 10 log ^- 10 log 



'A 



= R T + A - 10 log J -70.9. 

 "a 



pclO' 

 1^¥ 



2. There was also given the relation between the 

 calculated threshold and the receiving response 

 Rj; in equation (18) 



T = 10 logr- 194.9 - R„. 



