Resonance Frequency Of Transducer Research Articles

Study of vibrational characteristics for piezoelectric sandwich ultrasonic transducers

Electro-acoustic efficiency is an important parameter for high power ultrasonic transducers. When a transducer is acoustically matched into its load, the electro-acoustic efficiency reaches the potential efficiency, which depends only on the transducer's unloaded parameters, not on the acoustic load. The relation between the potential efficiency and the contacting loss caused by bonding at interfaces and the relation between the potential efficiency and the dimensions of the end sections of the sandwich transducer are examined. The effects of the loss at the contacting surfaces on the transducer's resonant frequency and the potential efficiency are studied. The results show that there is an optimum design of the sandwich transducer which maximizes the potential efficiency and minimizes the effect of the contacting loss on the transducer's resonant frequency.

A Helmholtz resonator model for an electrostatic ultrasonic air transducer with a V-grooved backplate

Abstract A model for the resonance frequency of an electrostatic ultrasonic air transducer with a uniformly grooved backplate is described based on the Helmholtz resonator theory. The resonance frequency of the transducer can be determined from the shape and dimensions of the backplate's grooves and the membrane's characteristics. In the case of a V-grooved backplate, the depth of the groove and the mass per unit area of the membrane are the parameters that determinate the resonance frequency. Experimental results suggest that the tension of the membrane seems to have only a very weak influence on the resonance frequency.

Quantifying sonochemistry: Casting some light on a ‘black art’

Despite the ever increasing usage of power ultrasound to enhance reactivity in synthetic chemistry, many experimentalists experience difficulty in reproducing the work of other groups. Although such problems are most commonly encountered with chemical reactions which have been performed in ultrasonic baths, even reactions involving probe systems have sometimes proved difficult to reproduce. The origin of many of tehse problems can be traced to a failure of the original report to specify the exact sonication conditions, e.g. the frequency of ultrasonic irradiation, the precise power entering the reaction system, the geometry of the reaction vessel, the presence of a bubbled gas or even the temperature of the reaction ∗. In this article we report the results of some model reactions performed using the newly developed Undatim Sonoreactor probe system. This particular instrument is equipped with an automatic transducer resonance frequency search device, enabling the power input to a system to be maintained accurately throughout a reaction, thereby offering considerable advantages over the normal commercially available equipment in terms of both the monitoring and control of irradiation parameters. Using this facility we are able to report how ultrasonic energy input to a chemical reaction is affected by the following important reaction parameters: ultrasonic power used, the presence of bubbled gas, temperature, solvent composition and reaction volume. In addition, a comparison is made of the ultrasonic power available from three different laboratory sonicators operating at a nominal frequency of 20 kHz.

The contractile response during steady lengthening of stimulated frog muscle fibres.

1. Steady lengthenings at different velocities (0.025-1.2 microns/s per half-sarcomere; temperature 2-5.5 degrees C) were imposed on isolated frog muscle fibres at the isometric tetanus plateau by means of a loudspeaker motor. The lengthening at the sarcomere level was measured by means of a striation follower either in fixed-end or in length-clamp mode. The force response was measured by a capacitance gauge transducer (resonance frequency 50 kHz). Preparations showing gross non-homogeneity during lengthening were excluded. 2. A steady tension was in all cases reached after about 20 nm per half-sarcomere of lengthening. Tension during this steady phase rose with speed of elongation up to 0.25-0.4 micron/s per half-sarcomere, when tension was 1.9-2 times isometric tetanic force (T0). Further increase in speed produced only very little increase in the steady tension. 3. During the transitory phase, before steady tension was reached, the tension rose monotonically if speed of lengthening was less than 0.25-0.3 micron/s per half-sarcomere; at higher speed the tension rose above the steady level, reaching a peak when extension was 10-14 nm per half-sarcomere, and then fell to the steady level. Tension at the peak continued to rise with speed of lengthening above 0.3 micron/s per half-sarcomere. 4. During the tension rise within the transitory phase of force response the segment elongated at a speed 15-20% lower than that imposed on the whole fibre, as a consequence of tendon compliance. 5. During the steady phase, non-homogeneity of lengthening speed began above a speed of lengthening which varied from fibre to fibre. At speeds below this value, segments elongated at the same speed as that imposed on the fibre. 6. Tension responses to large step stretches (up to 12 nm per half-sarcomere), applied at the plateau of isometric tetanus, showed that the instantaneous elasticity of contractile machinery is not responsible for the limit in force attained with high-speed lengthening. 7. Instantaneous stiffness was determined during the steady state of force response by superposing small steps (less than 1.5 nm per half-sarcomere) on steady lengthening at different velocities. Stiffness was 10-20% larger during lengthening than at the plateau of isometric tetanus and remained practically constant, independent of lengthening velocity, in the range of velocities used. 8. The results indicate that steady lengthening of a tetanized fibre induces a cross-bridge cycle characterized by fast detachment of the cross-bridge extended beyond a critical level.(ABSTRACT TRUNCATED AT 400 WORDS)

Analysis of the ultrasonic beam produced by a wedge transducer

Recently, the wedge transducer has found application in ultrasonic microscopy (J. D. N. Cheeke and L. Germain, IEEE Ultrasonics Symposium, Montreal, 1989). Since the resonance frequency of the wedge transducer varies with position, it is possible to sweep the ultrasonic beam by changing the driving frequency. A theoretical analysis is given of the diffraction pattern produced at a single frequency by a one‐dimensional wedge transducer. The relation of resonance frequency with position is by no means linear, which means that the distribution of resonance frequency along the transducer is not symmetric about its center position. A linear relationship between beam frequency and position on the wedge is possible if one uses a curved back surface, however. The effect of the transducer edge on the diffraction pattern is noticeable even at frequencies at which the beam emerges near the center of the wedge. This result is confirmed by comparing with schlieren photographs. The implication of this observation for design of Gaussian transducers is considered. [Research supported by the Office of Naval Research.]

Measurement of the effective velocity amplitude of a weakly focussed bowl ultrasonic transducer

The possibility of determining the surface velocity of an ideal focussed bowl source as a function of frequency from pressure measurements at one axial field position is identified. Consideration is given to the non-ideal case by the inclusion of an effective geometrical depth for the bowl transducer. A set of measurements is presented which indicate that the value of the transducer resonant frequency obtained is little affected by the effective depth of the bowl. Results of the effective velocity distributions as functions of frequency for a set of three transducers, nominally identical except for the backing conditions, are also presented together with electrical impedance plots. The method proposed is a simple procedure for use in the monitoring of transducer production and for identifying the frequencies at which the transducers may be most effectively operated.

Mechanical spring having negative spring stiffness useful in an electroacoustic transducer

A mechanical spring with negative spring stiffness adapted for use in an electroacoustic transducer unit for reducing the transducer resonant frequency. The mechanical spring with negative spring stiffness comprises two blade springs having both ends coupled to each other and which, under the influence of a compressive force F which acts in a direction along an imaginary line through both ends of the mechanical spring, are each bent in one of two opposite directions.

Characterization of length expander magnetostrictive rare earth‐iron rods under normal use conditions in transducers

Magnetostrictive rare earth‐iron rods are presently mainly used as active elements of emission transducers. In this case, rods are mechanically prestressed and magnetically polarized. They are excited at high level around the transducer resonance frequency, which is much lower than the rod natural frequency. In order to characterize the rods under these conditions, a two‐rod device has been designed, on which the electrical impedance has been measured before being processed by a computer program. The results are the longitudinal piezomagnetic constants of the alloy. The program is based on a plane‐wave model; its assumptions on eddy currents and leakage flux are discussed with respect to results provided by a finite element computation. Coupling coefficient k33, Young's modulus, permeability, and loss terms have been reckoned using this method for alloys of various origins and are presented. The characterization of materials started with L. Néel's laboratory alloy [J. Acoust. Soc. Am. Suppl. 1 81, S89 (1987)] and is carried on with grain‐oriented alloys.

Electroacoustic transducer unit with reduced resonant frequency and mechanical spring with negative spring stiffness, preferably used in such a transducer unit

An electroacoustic transducer unit comprises an electroacoustic transducer with a diaphragm (1), a magnet system (2) with an air gap (3), and a voice-coil former (4) with a voice coil (5) arranged in the air gap (3) of the magnet system. The transducer unit comprises means for reducing the transducer resonant frequency including mechanical springs with negative spring stiffness each coupled between a stationary part of the transducer unit and a movable part, for example the voice-coil former or the diaphragm of the transducer (FIG. 1b). The transducer unit further comprises a control device (42) which generates a control signal for correcting the position of the diaphragm. The mechanical spring with negative spring stiffness comprises two blade springs with both ends coupled to each other and which, under the influence of a compressive force F which acts in a direction along an imaginary line through both ends of the mechanical spring, are each bent in one of two opposite directions.

A strain-gauge myograph for isometric measurements of tension in isolated small blood vessels and other muscle preparations

Isometric tension measurements in vitro on small vessels are important in studies of pharmacodynamic vascular effects of drugs and autacoids. The present study describes a precision myograph equipped with a newly constructed highly isometric strain-gauge transducer used in conjunction with a very sensitive, low-noise and virtually drift-free dc-amplifier. The isometric quotient of the transducer, defined as deflection in micrometer per g of force, is about 5.2. The transducer resonance frequency is 341 c sec with a damping constant of 1.05. The highest sensitivity of the transducer in connection with the matching dc-amplifier is about 170 mVg/V force. The practical working range of the myograph is from 2 mg to about 10 g of applied tensile force. Tubular segments of vessels with internal diameters down to 150 μm can be mounted in the myograph on two stainless-steel pins submerged in a 5 ml preparation bath. Precise mounting and setting of passive (resting) tension is assured by the use of micrometer-equipped adjustable miniature mounting tables suspended by roller bearings. The myograph may be provided with electrodes for field-effect stimulation of the vessel preparations. Other muscle preparations may also be mounted in the myograph. Application of the myograph in studies on rabbit coronary arteries is demonstrated by a length-tension diagram obtained in experiments with tubular segments (inner diameter about 500 μm) of the circumflex branch on the left coronary artery, which shows a typical course in development of active and passive tension of the smooth musculature when exposed to alternating potassium depolarization and increasing mechanical stretching. The potassium contracture of the coronary vessels and the log-concentration/response relationship at accumulating potassium concentrations were also investigated.

Stiffness and force in activated frog skeletal muscle fibers

Single fibers, isolated intact from frog skeletal muscles, were held firmly very near to each end by stiff metal clasps fastened to the tendons. The fibers were then placed horizontally between two steel hooks inserted in eyelets of the tendon clasps. One hook was attached to a capacitance gauge force transducer (resonance frequency up to approximately 50 kHz) and the other was attached to a moving-coil length changer. This allowed us to impose small, rapid releases (complete in less than 0.15 ms) and high frequency oscillations (up to 13 kHz) to one end of a resting or contracting fiber and measure the consequences at the other end with fast time resolution at 4 to 6 degrees C. The stiffness of short fibers (1.8-2.6 mm) was determined directly from the ratio of force to length variations produced by the length changer. The resonance frequency of short fibers was so high (approximately 40 kHz) that intrinsic oscillations were not detectably excited. The stiffness of long fibers, on the other hand, was calculated from measurement of the mechanical resonance frequency of a fiber. Using both short and long fibers, we measured the sinusoids of force at one end of a contracting fiber that were produced by relatively small sinusoidal length changes at the other end. The amplitudes of the sinusoidal length changes were small compared with the size of step changes that produce nonlinear force-extension relations. The sinusoids of force from long fibers changed amplitude and shifted phase with changes in oscillation frequency in a manner expected of a transmission line composed of mass, compliance, and viscosity, similar to that modelled by (Ford, L. E., A. F. Huxley, and R. M. Simmons, 1981, J. Physiol. (Lond.), 311:219-249). A rapid release during the plateau of tetanic tension in short fibers caused a fall in force and stiffness, a relative change in stiffness that putatively was much smaller than that of force. Our results are, for the most part, consistent with the cross-bridge model of force generation proposed by Huxley, A. F., and R. M. Simmons (1971, Nature (Lond.), 213:533-538). However, stiffness in short fibers developed markedly faster than force during the tetanus rise. Thus our findings show the presence of one or more noteworthy cross-bridge states at the onset and during the rise of active tension towards a plateau in that attachment apparently is followed by a relatively long delay before force generation occurs. A set of equations is given in the Appendix that describes the frequency dependence of the applied sinusoid and its response. This model predicts that frequency dependent changes can be used as a measure of a change in stiffness.

Determination of Ultrasonic Absorption and Velocity and the Derived Thermodynamic Properties of Pure and Binary Molten Salts

The absorption and velocity of ultrasonic waves in molten salts are studied with an improved pulse method, which allows an exact and immediate measurement of the runtime of the impulses and of the amplitude of the recorded signals. The measurements are performed in the pure molten salts sodium nitrate, potassium nitrate, and silver nitrate as well as in the three binary mixtures of these salts in the temperature range between 430 K and 620 K at various compositions. All values are measured at 27.789 MHz, the resonance frequency of the quartz transducers being used. From the ultrasonic velocity, together with the expansion coefficient and the specific heat capacity, the adiabatic compressibility, the adiabactic constant, and the Rao's constant have been calculated. From the ultrasonic absorption and velocity results the volume viscosity, which can be referred to the structural relaxation of the molecules in the fused salts investigated here.

A 10 mus component in the tension transients of isolated intact skeletal muscle fibres of the frog.

The transients of the tension and the angle of a first order diffraction line of isolated single intact muscle fibres of the M. lumbricalis IV of the foot resulting from rapid length changes have been measured. Furthermore simulations of the tension transients, taking the resonance frequency of the force transducer, the inertia of the fibre and the influence of the surrounding fluid into account, are presented. The tension transients could be simulated by a system of continuous elements with undamped elasticity - Young's modulus E1 = 1.8 X 10(8) N/m2 - in series with elasticity E2 = 5.4 X 10(7) N/m2 parallel to a damping element - coefficient of damping mu = 2,300 Ns/m2; yielding a relaxation time of 10 mus. The Young's modulus of the undamped series elasticity E1 implies that a sudden shortening of 2 nm per half sarcomere should reduce the active tension to zero. The results obtained from the diffraction pattern recording show that the displacement in the fibre is in accordance with the relative length change caused by the displacement generator. It is therefore believed that the tendon and tendon-muscle junction are sufficiently stiff to allow ascribing the above-mentioned elasticity and damping to the fibre itself.

Preliminary design rationale for tonpilz transducer elements

Analysis methods for the prediction of performance parameters for tonpilz transducer elements are quite common. Given a physical design, the methods of equivalent circuit analysis, one‐dimensional plane‐wave modeling, or finite element modeling each gives useful approximations of increasing accuracy. However, none of these methods can provide a design from a given set of performance requirements. They are analysis methods rather than design methods. This paper presents a rationale for the development of a preliminary design method for tonpilz transducer elements. The algorithm requires input values for the transducer resonant frequency, 3‐dB bandwidth, radiated power level, and beamwidth. The output is a simple tonpilz element consisting of a head mass, a tail mass, a ceramic stack with minimum volume, and a stress rod if desired.

System for precisely and economically adjusting the resonance frequency of electroacoustic transducers

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Frequency Analysis of Pulsed Optoacoustic Signals and the Application to Chemical Analysis

The optoacoustic signal generated via pulsed laser excitation-transducer detection is frequency analyzed via a discrete Fourier transform. The frequency spectrum is found to exhibit a pronounced maximum at the transducer resonant frequency. Use of this maximum as a measure of the optoacoustic signal strength allows for discrimination against window absorption and various electrical and mechanical noise sources.

The elastic problem of the flattened-cylinder type of underwater acoustical compliance element

Sealed tubes containing a gas are often used in oil-filled underwater transducers to provide extra acoustical compliance beyond that of the oil. One type consists of a flattened circular cylinder. An analysis of this family of pressure release tubes is made to provide expressions for the three important characteristics: (1) the compressibility, (2) the pressure at which stress failure of the material occurs, and (3) the pressure at which the two flattened sides come together, ending the usefulness of the device. These quantities are calculated for a particular tube as an example. The effect of initial pressurization is included. Pressurized tubes were used in a transducer test. Fair agreement is found between measured shift in transducer resonant frequency with depth, and the shift calculated from compressibility change with depth.

Internal losses in polyvinylidene fluoride (PVF2) ultrasonic transducers

The dielectric and acoustic losses in oriented PVF2 have been measured from 0.1 MHz to 100 MHz and from 1.5 MHz to 39 MHz, respectively, in the direction perpendicular to the stretching direction at room temperature. A broad absorption peak located at around 5 MHz is observed in each case. The locations of these absorption peaks are of great disadvantage for ultrasonic transducer fabrication. The longitudinal acoustic velocity in the direction perpendicular to the stretching direction is also measured from 1.5 MHz to 39 MHz at room temperature. It is found that the velocity increases monotonically in this frequency range. As a result, the resonance frequency of a PVF2 transducer will be affected proportionally.

Application of the USRD type E8 transducer as an acoustic parametric source

The USRD type E8 transducer was operated as an acoustic parametric source, and its performance as such was measured in two separate laboratory experiments and at sea. The parametric source was driven by a primary signal that consisted either of two high-frequency components or of an amplitude-modulated high-frequency carrier. The primary signal was centered at the transducer resonance frequency near 1.4 MHz, and the observed difference frequencies ranged from 20 to 200 kHz. During typical operation the primary electrical signal had a total power of approximately 6 W, and a difference-frequency signal at 50 kHz had a source level of about 154 dB re 1 μPa m. This paper describes the design and performance of the parametric source. It also presents a sequence of radiation patterns and values of beamwidth that illustrate difference-frequency beam formation in the nearfield of the parametric source.

Analysis of the Pulse-Superposition Method for Measuring Ultrasonic Wave Velocities as a Function of Pressure and Temperature

A discussion is given of the merits of a pulse-superposition method for determining ultrasonic-wave velocities in single crystals as a function of pressure and temperature. For this method [H. J. McSkimin, J. Acoust. Soc. Am. 33, 12 (1961)], the wave frequency is continuously matched to the resonance frequency of the crystal transducer in order to minimize the effect of coupling to the transducer. Ratios of velocities can be determined to within one part in ten thousand. Illustrative data are shown for crystal quartz in the pressure range 14.5 to 30 000 psi at both 25.0° and −195.8°C.