Patent Publication Number: US-3879698-A

Title: Unipolar acoustic pulse generator apparatus

Description:
United States Patent [1 1 Pepper UNIPOLAR ACOUSTIC PULSE GENERATOR APPARATUS [75] Inventor: Perry Arnold Pepper, Great Neck,  
 [2|] Appl. N0.: 354,519  
 [52] U.S. Cl 340/5 R; IMO/8.1; 340/10; 340/l5 [5 l] Int. Cl. H04b 11/00 8 Field of Search 340/3 A, 5 R, l0, l5;  
 [451 Apr. 22, 1975 3,7l5,7l0 2/l973 Bernstein et al 340/l5 X Primary Examiner-Richard A. Farley Attorney, Agent, or Firm-Daniel H. Steidl [57] ABSTRACT In apparatus for producing a unipolar displacement of the radiating face of an electroacoustic transducer to generate unipolar accoustic pulses in an acoustic medium, the dimensions of the radiating face of the transducer or of an array of radiating transducer faces are chosen to simplify the response of the transducers, thereby simplifying the required transducer driving signals and the apparatus required to generate those signals.  
 [56] References Cited UNITED STATES PATENTS 50 Claims, 6 Drawing Figures REP-RgTE 30 ei&#39;ifim LOW PASS TRANSDUCER FILTER mammmzl 225% A&amp;\. 1! J94 AW-Z 2550 &amp;&#39;  
 ffl-Z PULSE aeuerwua PATENTEDAPR22 I975 sum 1 5 z FIG. IA FIG I B DI5PLA CEMENT FIG2A I i 1 E t 2t, st.  
 ADDITIONAL SIGNAL COMPONENT F B u I A I 2t0 31 t T&#39;ME PATENTEU APRZZIQIS sum 2 B52 QUE  mwaa mEKKwZm-w Esau: mm  
 EPEFZmHmnEE UNIPOLAR ACOUSTIC PULSE GENERATOR APPARATUS BACKGROUND OF THE INVENTION This invention relates to electroacoustic transducer apparatus and, more particularly, to eiectroacoustic transducer apparatus for producing high energy unipolar pressure pulses in an acoustic medium of relatively high specific impedance (e.g., water).  
  Unipolar acoustic pulses are useful in a wide variety of applications. In underwater sonar, for example, uni polar acoustic pulses radiating from a transducer can be used for high resolution object detection, identification, and the like. Unipolar acoustic pulses are typically generated by producing a unipolar displacement of the radiating face of a transducer device (e.g., an electroacoustic transducer device) which is immersed in or otherwise contiguous with an acoustic medium. In general, the unipolar displacement of the radiating transducer face (sometimes referred to herein as a unipolar transducer displacement or unipolar transducer response) results in a sequence of unipolar acoustic pulses in the acoustic medium. The individual pulses in such a sequence do not generally correspond to the amplitude and duration of the unipolar transducer displacement. Rather, the sequence of the acoustic pulses usually corresponds more nearly to the second derivative of the displacement of the radiating transducer face (i.e., the acceleration history of the radiating transducer face). Unipolar transducer displacements are emdployed not because they uniquely result in unipolar acoustic pulses, but because the acoustic pulse sequences produced are relatively uncomplicated and of short duration (i.e.. not substantially longer than the transducer displacement pulse). This latter feature is particularly desirable for pulse repetition purposes. In reading this specification, the distinction between unipolar transducer displacement and unipolar acoustic pulses must be kept clearly in mind.  
  In copending U.S. patent application Ser. No. 92,798 now U.S. Pat. No. 3,715,7l0, J. Bernstein, et al.. disclose apparatus for producing unipolar displacement of the radiating face of an electro-acoustic transducer. In accordance with the principles of that invention, a transducer (e..g., a cylindrical piezo-electric transducer) is driven by an electrical signal having discontinuities in amplitude which initially stimulate vibration or mechanical oscillation of the transducer and then, after a half cycle of transducer oscillation in the fundamental mode. substantially dampen the oscillations of the transducer. Transducer oscillations are damped by applying signal discontinuities to the transducer which would produce oscillations of the same amplitude as the oscillations to be damped, but in phase opposition thereto, thereby interfering with and tending to cancel out the undesired oscillations. Since transducers of the type described may exhibit more than one mode of vibration in each physical direction, it is appropriate to provide a driving signal having discontinuities for damping oscillation in several of the more significant modes in order to produce a clean (i.e., sharply defined) unipolar transducer response. In general, even for very simply shaped transducer responses, the required driving voltage waveforms are quite complex and so will be the electrical or electronic apparatus used to generate these waveforms.  
  In my concurrently filed application Ser. No. 354,5 l 8, it is shown that for certain types of transducer responses, the transducer driving signal can be considerably simplified by relating the time parameter of the desired transducer response to the longitudinal dimension of the transducer.  
  In certain situations it becomes necessary to consider the pressure of the acoustic medium on the radiating face of the transducer. This is particularly true when the acoustic medium has a relatively high value of specific impedance, as is true, for example, in the case of water. In that event. an additional driving signal component must be provided to account for the interaction of the transducer and the acoustic medium.  
  It is therefore an object of this invention to improve and simplify unipolar acoustic pulse generating apparatus for use with acoustic media of relatively high specific impedance.  
  It is a more particular object ofthis invention to provide unipolar acoustic pulse generating apparatus in which the additional transducer driving signal component required to account for the pressure of the acoustic medium on the radiating face of the transducer is simplified and the driving signal generating apparatus is also accordingly simplified.  
 SUMMARY OF THE INVENTION These and other objects of the invention are accomplished in accordance with the principles of the invention by unipolar acoustic pulse generator apparatus in which a certain dimension of the radiating face of the transducer or of the several radiating faces of an array of transducers is chosen to simplify the response of the transducers, thereby simplifying the required driving signals and the apparatus required to generate those signals. More particularly, the greatest or principal dimension z of the radiating transducer face or array of faces is chosen so that a time parameter I of the desired unipolar acoustic output pulse is substantially equal to the quotient z/(,,-. where 0,, is the acoustic velocity of the ensonified acoustic medium.  
  Further features and objects of the invention, its nature and various advantages will be more apparent upon consideration of the attached drawing and the following detailed description of the invention.  
 BRIEF DESCRIPTION OF THE DRAWING FIG. IA is a side view of a piezoelectric transducer of the type used for generating unipolar acoustic pulses in an acoustic medium;  
 FIG. 1B is an end view of the transducer of FIG. 1A;  
  FIG. 2A is a diagram of an idealized unipolar displacement of the radiating face of the transducer of FIG. I plotted against time;  
  FIG. 2B is a diagram of the additional transducer driving signal component required to account for the pressure of the acoustic medium on the radiating face of the transducer in unipolar acoustic pulse generator apparatus constructed in accordance with the principles of this invention;  
  FIG. 3 is a schematic block diagram of apparatus for generating transducer driving signals of the type shown in FIG. 2B; and  
  FIG. 4 is an end view of an array of transducers useful in understanding the application of the principles of this invention to transducer arrays.  
 DETAILED DESCRIPTION OF THE INVENTION As shown in FIGS. 1A and 18, a typical cylindrical electroacoustic transducer is made up of a plurality of discs 12 interspersed with electrodes 14 and bonded together with adhesives or the like. Discs I2 are a piezoelectric material (e.g., barium titanate or lead zirconate titanate) polarized to operate in the 33 mode wherein the mechanical stresses in the transducer material are parallel to the longitudinal axis l6 of the transducer and perpendicular to the electrodes. Electrodes 14 are interconnected by wellknown wiring arrangements (not shown).  
  Transducer 10 has a radiating face I8 contiguous with an acoustic medium (e.g., air or water) and an op posite non-radiating face 20. The non-radiating face of transducer 10 is shown as free. but it may be clamped, attached to springs, or otherwise restrained in any manner.  
  When transducer 10 is energized by a suitable driving signal applied to electrodes 14, radiating face 18 displaces, thereby projecting an acoustic signal into the surrounding acoustic medium. In many applications, the most desirable acoustic signal is a unipolar pulse. As is discussed in greater detail in my above-mentioned concurrently filed application, unipolar acoustic pulses are most readily generated by producing a unipolar displacement of the radiating face of the transducer, as illustrated, for example, by the displacement history of FIG. 2A. Although the particular displacement history shown in FIG. 2A is not necessarily the most desirable in all applications and although the principles of this invention are equally applicable to generating a wide variety of other unipolar transducer responses, the present invention will be readily understood from an explanation of its application to generating a trans ducer response of the type shown in FIG. 2A.  
  Apparatus for producing displacement of the radiat ing face of a transducer of the type shown in FIG. 1 is disclosed in the above-mentioned application of Bernstein. et al., and in my above-mentioned concurrently filed application. The required transducer driving signal is typically a curved waveform having a number of discontinuities for initially stimulating and then damping oscillation of the transducer. A driving signal of this type is conveniently generated by summing a plurality of appropriately shaped and timed signal pulses. Appa ratus for generating a signal of this type is shown in FIG. 3. In the apparatus of FIG. 3, rep-rate signal generator and differentiator 32 produce a trigger signal whenever an acoustic output pulse is required. This trigger signal is applied to each ofa plurality of pulse generating signal channels, respectively represented by pulse generators 40-1 through 40-n. Each of pulse gen erators 40 produces an appropriately shaped and timed output signal pulse. The signal pulses produced by pulse generators 40 are scaled and summed by potentiometers S0 and operational amplifier 52 to produce a driving signal waveform applied to transducer 70. If desired, the output signal of amplifier 52 may be filtered by low pass filter 60 before being applied to transducer 70. Signal generating apparatus of the type shown in FIG. 3, is described in greater detail, for example, in my concurrently filed application.  
  As a rule, if the response of the transducer to driving signal discontinuities can be simplified, the quality of the acoustic output pulse is improved and the number of modes of transducer oscillation requiring damping is reduced. This results in simplification of the required transducer driving signal and of the apparatus required to generate that signal. As described in my concurrently filed application, a considerable simplification in the driving voltage waveform is achieved by designing the transducer so that the half pulse duration time parameter t of the desired output pulse is an integer multiple of the quotient L/c, where L is the longitudinal dimension of the transducer and c is the acoustic velocity of the material of the transducer. The quotient U0 is a time parameter which corresponds to the time required for an acoustic wave to propagate through the transducer along its length L.  
  In certain applications, interaction between the ensonified acoustic medium and the transducer becomes a significant factor in transducer response. This is particularly true when acoustic pulses are to be transmitted into a medium, such as water, which has a relatively high specific impedance value, this value being the product of the mass density of the medium and its acoustic velocity c In that event, an additional transducer driving signal component is required to account for the pressure of the medium on the radiating face of the transducer. While this additional signal component will in general have a distinctly smaller amplitude than those signal components considered, for example, in my concurrently filed application, it must still be pres ent in the driving signal waveform for accurate output pulse generation.  
  In general, the nature and complexity of the additional signal component referred to above depends on three time parameters: the half pulse duration time parameter l,,, the time required for an acoustic pulse to travel the length of the transducer (e.g., the quotient U0); and the time required for an acoustic wave in the ensonified medium to traverse the greatest or principal dimension of the radiating face of the transducer. The last of these parameters is given by the quotient z/c where z is the maximum dimension of the radiating face of the transducer and c is as defined above. As in my concurrently filed application, it is desirable for the purpose of simplifying this additional signal component to design the transducer so that I is an interger multiple of the quotient L/(&#39;, the relationship t L/c being the most desirable. In accordance with the principles of the instant invention, it is also desirable for this purpose to design the transducer so that t (z/c,,.). The simplest additional signal component is required when both of these conditions are met, i.e., when t (L/c) (ZICW).  
  In the case of the cylindrical transducer of FIG. 1, z is the diameter of radiating face 18. Assuming that t (Me) (2/0 for the transducer of FIG. 1 and that non-radiating face 20 is not constrained, the additional transducer driving signal component required for the generation of the output pulse shown in FIG. 2A takes the form shown in FIG. 2B. This waveform includes two pulses, each of duration t beginning respectively at l 0 and t 2! Each of these pulses includes an initial discontinuity followed by gradual decay. Between these two pulses, the signal waveform has a polarity opposite that of the peaks of pulses. Like the other components of the transducer driving signal, this additional driving signal component may be generated by one or more channels of the apparatus of FIG. 3, i.e., by one or more of pulse generators 40.  
  The principles discussed above in connection with cylindrical transducer of HG. l are equally applicable in a wide variety of other situations. In the case of an isolated cylindrical transducer of basic diameter d operating in the 33 mode and employing a circular radiating face of diameter d. it is d rather than d which should be used for z in the preceding relationships. This situation is exemplified by many practical transducer designs employing end masses.  
  For an isolated prismatic transducer of any general cross sectional shape operating in the 33 mode, is the maximum or greatest dimension of the radiating face. In the case of a transducer having a square or rectangular radiating face. for example, z is the diagonal of the square or rectangle. [n the case of a transducer having a triangular radiating face, 2 is the longest side of the triangle. ln the case of a transducer having an elliptical radiating face, 2 is the major axis of the ellipse.  
  In certain applications, it may be desired to produce transducer responses having different durations. For example, such responses may all have the form shown in FIG. 2A, but with different values of t as well as different amplitudes. in accordance with the foregoing principles of this invention. this capability is best achieved by use of a single transducer for each different response duration. Each transducer would then have a different radiating face dimension, 2. in accordance with the optimizing principle, 1 =c,.r,,, and, in accordance with the optimizing principle disclosed in my above-mentioned concurrently filed application, i.e.. L cl would have a different length, L.  
  The principles of this invention are also applicable to arrays of transducers having multiple radiating faces in a common plane. in the case ofsuch an array, the maximum dimension of the array of radiating faces corresponds to the maximum dimension of the radiating face of an isolated transducer and is the value of z in the relationships above. For the rectangular array of radiating faces 80 shown in FIG. 4, z is the diagonal of the array as indicated by the segment a b. As is evident from this example, the intervening portions of the nonradiating interstices 82 between the radiating faces 80 must be included in determining the distance 2.  
 What is claimed is:  
  1. Apparatus for producing a unipolar displacement of the radiating face of an electroacoustic transducer to produce an acoustic signal in a medium having an acoustic velocity c said unipolar displacement having a half pulse duration time parameter r, and said radiating face having maximum dimenion z, characterized in that 1,, is substantially equal to the quotient (z/c means for generating a signal waveform, and means for applying said signal waveform to said transducer.  
  2. Apparatus for producing a unipolar displacement of the radiating face of an electroacoustic transducer to produce an acoustic signal in a medium having an acoustic velocity c... said unipolar displacement having a half pulse duration time parameter r, and said radiating face having maximum dimension z, characterized in that t, is substantially equal to the quotient (z/c,,.) said radiating face of said transducer displacing from a rest position to maximum displacement during during a first interval of time t and returning from maximum displacement to said rest position during a second subsequent interval of time t and means for applying to said transducer an electrical signal including a signal component characterized by a first signal pulse at the start of said first time interval and a second signal pulse at the end of said second time interval.  
  3. The apparatus defined in claim 2 wherein each of said signal pulses is characterized by a substantially instantaneous rise time followed by gradual decay.  
  4. The apparatus defined in claim 3 wherein the rise time of said first signal pulse is substantially concurrent with the start of said first time interval and the rise time of said second signal pulse is substantially concurrent with the end of said second time interval.  
  5. The apparatus defined in claim 4 wherein the duration of each of said signal pulses is substantially equal to r,,.  
  6. The apparatus defined in claim 5 wherein said electrical signal component is further characterized by a predetermined reference signal level before said first signal pulse and after said second signal pulse.  
  7. The apparatus defined in claim 6 wherein the peaks of both of said signal pulses are of a first polarity relative to said predetermined reference signal level.  
  8. The apparatus defined in claim 7 wherein said electrical signal component is further characterized by a polarity opposite said first polarity during the interval of time between said first and second signal pulses.  
  9. The apparatus defined in claim 8 wherein the radiating face of said transducer is a circular surface of diameter z.  
  10. The apparatus defined in claim 9 wherein said transducer is a cylinder, one end of which is the radiating face of said transducer.  
  11. The apparatus defined in claim 8 wherein the radiating face of said transducer is a rectangle of diagonal z.  
  12. The apparatus defined in claim 8 wherein the radiating face of said transducer is a triangle having longest side 2.  
  13. The apparatus defined in claim 8 wherein the radiating face of said transducer is an ellipse having major axis 2.  
  14. The apparatus defined in claim 2 wherein said means for applying comprises:  
 means for generating a trigger signal;  
 a plurality of shaped pulse generating channels responsive to said trigger signal, each of said channels comprising means for delaying said trigger sig nal. means responsive to the delayed trigger signal for generating a rectangular pulse of predetermined amplitude and duration, and means for shaping said rectangular pulse to produce a shaped output pulse; and  
 means for summing the shaped output pulses of each of said channels to produce said electrical signal.  
  15. Apparatus for producing a unipolar displacement of the radiating face of an electroacoustic transducer to produce an acoustic signal in a medium having an acoustic velocity c... said unipolar displacement having a half pulse duration time parameter I, and said radiating face having a maximum dimension 1. characterized in that r, is substantially equal to the quotient (z/cw), said transducer being characterized by an acoustic velocity r, wherein the dimension L of said transducer normal to said radiating face bears substantially the same proportional relation to c as 2 bears to c... and wherein the radiating face of said transducer displaces from a rest position to maximum displacement during a first interval of time r, and returns from maximum displacement to said rest during a second subsequent interval of time i means for applying to said transducer an electrical signal including a signal component characterized by a first signal pulse at the start of said first time interval and a second signal pulse at the end of said second time interval.  
  16. The apparatus defined in claim wherein each of said signal pulses is characterized by a substantially instantaneous rise time followed by gradual decay.  
  T7. The apparatus defined in claim 16 wherein the rise time of said first pulse is substantially concurrent with the start of said first time interval and the rise time of said second signal pulse is substantially concurrent with the end of said second time interval.  
  18. The apparatus defined in claim 17 wherein the duration of each of said signal pulses is substantially equal to t 19. The apparatus defined in claim 18 wherein said electrical signal component is further characterized by a predetermined reference signal level before said first signal pulse and after said second signal pulse.  
  20. The apparatus defined in claim l9 wherein the peaks of both of said signal pulses are the first polarity relative to said predetermined reference signal level.  
  21. The apparatus defined in claim 20 wherein said electrical signal component is further characterized by a polarity opposite said first polarity during the interval of time between said first and second signal pulses.  
  22. The apparatus defined in claim 21 wherein the radiating face of said transducer is a circular surface of diameter 23. The apparatus defined in claim 22 wherein said transducer is a cylinder of length L. one end of which is the radiating face of said transducer.  
  24. The apparatus defined in claim 15 wherein said means for applying comprises:  
 means for generating a trigger signal;  
 a plurality of shaped pulse generating channels responsive to said trigger signal. each of said channels comprising means for delaying said trigger signal. means responsive to the delayed trigger signal for generating a rectangular pulse of predetermined amplitude and duration, and means for shaping said rectangular pulse to produce a shaped output pulse. and  
 means for summing the shaped output pulses of each of said channels to produce said electrical signal.  
  25. Apparatus for producing a unipolar displacement of the radiating face of an electroacoustic transducer to produce an acoustic signal in a medium having an acoustic velocity 0,... the radiating face of said transducer having maximum dimension 2 and said transducer having an acoustic velocity and a dimension L normal to said radiating face, wherein the ratio of z to c is substantially equal to the ratio of L to c, means for generating a signal waveform, and means for applying said signal waveform to said transducer.  
  26. Apparatus for producing a unipolar displacement of the radiating face of an electroacoustic transducer to produce an acoustic signal in a medium characterized by an acoustic velocity c,,. said unipolar displacement having a half pulse duration time parameter t the radiating face of said transducer having maximum dimension 2. and said transducer having an acoustic velocity c and a dimension L normal to said radiating face, wherein I is substantially equal to the quotient (Mr) and to the quotient (z/c means for generating a signal waveform, and means for applying said signal waveform to said transducer.  
  27. Apparatus for producing a unipolar displacement of the radiating face of an electroacoustic transducer to produce an acoustic signal in an acoustic medium, said unipolar displacement having a half pulse duration time parameter t characterized in that t is substantially equal to the time required for an acoustic wave to traverse the maximum dimension of the radiating face through the acoustic medium, means for generating a signal waveform, and means for applying said signal waveform to said transducer.  
  28. Apparatus for producing a unipolar displacement of the radiating face of an electroacoustic transducer to produce an acoustic signal in an acoustic medium, said transducer having a non-radiating face opposite said radiating face. said unipolar displacement having a half pulse duration time parameter 1 characterized in that 1,, is substantially equal to the time required for an acoustic wave to travel through the transducer from one face to the other and further characterized in that I is substantially equal to the time required for an acoustic wave to traverse the maximum dimension of the radiating face through the acoustic medium, means for generating a signal waveform, and means for applying said signal waveform to said transducer.  
  29. Apparatus for generating a unipolar displacement of the radiating faces of a plurality of electroacoustic transducers to produce an acoustic signal in a medium having an acoustic velocity c said unipolar displacement having a half pulse duration time parameter t the radiating faces of said transducers forming a coplanar array having a maximum dimension 2 characterized in that 1,, is substantially equal to the quotient (LI/C means for generating a signal waveform. and means for applying said signal waveform to said transducers.  
  30. The apparatus defined in claim 29 wherein the radiating faces of said transducers displace from a rest position to maximum displacement during a first interval of time t and return from maximum displacement to said rest position during a second subsequent interval of time t,,.  
  31. The apparatus defined in claim 29 wherein each of said transducers is characterized by an acoustic velocity c and wherein the dimension L of each of said transducers normal to its radiating face bears substantially the same proportional relation to c as z bears to 32. The apparatus defined in claim 31 wherein the radiating faces of said transducers displace from a rest position to maximum displacement during a first interval of time 1., and return from maximum displacement to said rest position during a second subsequent interval of time t,,.  
  33. The apparatus defined in claim 32 comprising means for applying to said transducers an electrical signal including a signal component characterized by a first signal pulse at the start of said first time interval and a second signal pulse at the end of said second time interval.  
  34. The apparatus defined in claim 33 wherein each of said signal pulses is characterized by a substantially instantaneous rise time followed by gradual decay.  
  35. The apparatus defined in claim 34 wherein the rise time of said first signal pulse is substantially concurrent with the start of said first time interval and the rise time of said second signal pulse is substantially concurrent with the end of said second time interval.  
  36. The apparatus defined in claim 35 wherein the duration of each of said signal pulses is substantially equal to l,,.  
  37. The apparatus defined in claim 36 wherein said electrical signal component is further characterized by a predetermined reference signal level before said first signal pulse and after said second signal pulse.  
  38. The apparatus defined in claim 37 wherein the peaks of both of said signal pulses are of a first polarity relative to said predetermined reference signal level.  
  39. The apparatus defined in claim 38 wherein said electrical signal component is further characterized by a polarity opposite said first polarity during the interval of time between said first and second signal pulses.  
  40. The apparatus defined in claim 33 wherein said means for applying comprises:  
 means for generating a trigger signal;  
 a plurality of shaped pulse generating channels responsive to said trigger signal. each of said channels comprising means for delaying said trigger signal for generating a rectangular pulse of predetermined amplitude and duration, and means for shaping said rectangular pulse to produce a shaped output pulse; and  
 means for summing the shaped output pulses of each of said channels to produce said electrical signal.  
  41. Apparatus for producing a unipolar displacement of the radiating faces of a plurality of electroacoustic transducers to produce an acoustic signal in a medium having an acoustic velocity c said unipolar displacement having a half pulse duration time parameter I the radiating faces of said transducers forming a coplanar array having a maximum dimension z, each of said transducers having an acoustic velocity r&#34; and a dimension L perpendicular to its radiating face. wherein 1,, is substantially equal to the quotient (U) and to the quotient means for generating a signal waveform, and means for applying said signal waveform to said transducers.  
  42. Apparatus for producing a unipolar displacement of the radiating faces of a plurality of electroacoustic transducers to produce an acoustic signal in an acoustic medium, said unipolar displacement having a half pulse duration time parameter t the radiating faces of said transducers forming a coplanar array having a maximum dimension z. each of said transducers having a non-radiating face opposite said radiating face, characterized in that I, is substantially equal to the time required for an acoustic wave to propagate through each of said transducers from one of its faces to the other and further characterized in that 1., is substantially equal to the time required for an acoustic wave to prop agate a distance 1 in the acoustic medium, means for generating a signal waveform, and means for applying said signal waveform to said transducers.  
  43. Apparatus for generating a unipolar acoustic displacement of the radiating faces of a plurality of electroacoustic transducers, to produce an acoustic signal in a medium having an acoustic velocity c said unipolar displacement having a half pulse duration time parameter r the radiating faces of said transducers forming a coplanar array having a maximum dimension z characterized in that r, is substantially equal to the quotient (zlc the radiating faces of said transducers displacing from a rest position to maximum displacement during a first interval of time t and returning from maximum displacement to said rest position during a second subsequent interval of time t and means for applying to said transducers an electrical signal including a signal component characterized by a first signal pulse at the start of said first time interval and a second signal pulse at the end of said second time interval.  
  44. The apparatus defined in claim 43 wherein each of said signal pulses is characterized by a substantially instantaneous rise time followed by gradual decay.  
  45. The apparatus defined in claim 44 wherein the rise time of said first signal pulse is substantially con current with the start of said first time interval and the rise time of said second signal pulse is substantially concurrent with the end of said second time interval.  
  46. The apparatus defined in claim 45 wherein the duration of each of said signal pulses is substantially equal to t 47. The apparatus defined in claim 46 wherein said electrical signal component is further characterized by a predetermined reference signal level before said first signal pulse and after said second signal pulse.  
  48. The apparatus defined in claim 47 wherein the peaks of both of said signal pulses are of a first polarity relative to said predetermined reference signal level.  
  49. The apparatus defined in claim 48 wherein said electrical signal component is further characterized by a polarity opposite said first polarity during the interval of time between said first and second signal pulses.  
  50. The apparatus defined in claim 43 wherein said means for applying comprises:  
 means for generating a trigger signal;  
 a plurality of shaped pulse generating channels responsive to said trigger signal, each of said channels comprising means for delaying said trigger signal, means responsive to the delayed trigger signal for generating a rectangular pulse of predetermined amplitude and duration, and means for shaping said rectangular pulse to produce a shaped output pulse; and  
 means for summing the shaped output pulses of each of said channels to produce said electrical signal.