Due to the high acoustic impedance of the liquid that requires relatively small amplitudes of vibration in the medium to produce high acoustic power levels, it is relatively easy to generate high-intensity sound energy under water.
The attenuation of ultrasonic sound in water is much less than the sound attenuation in air, and this factor makes it possible to transmit high-intensity underwater sound over large distances.
Since the comparatively low acoustic impedance of the medium requires relatively large amplitudes of vibration, the generation of high-intensity sound fields in air is considerably limited. However, there are practical limitations in the large amplitudes of vibration, which may be produced by ultrasonic transducers.
Two of the most critical limitations are enforced (i) through the maximum stress that may be safely allowed in the vibrating element without fatigue failure; and (ii) through the harmonic distortion produced in the air when the peak acoustic pressure is a substantial fraction of atmospheric pressure.
Some basic design data will be presented for use in air which will help the reader to quantitatively understand the different connections between some of the fundamental parameters that control the production and transmission of ultrasonic sound in air.
Longitudinal Resonant Vibrators
There are three basic types of electromechanical transducers (Figure 1) that are generally used to convert continuous electrical oscillations into mechanical vibrations in order to produce acoustic power from the radiating end faces of the vibrating structures.
Figure 1. Examples of electroacoustic transducers for operating at longitudinal resonance.
In general, magnetostriction transducers used at ultrasonic frequencies use a large number of thin nickel laminations, each with a thickness of few thousandths of an inch, bonded together to form a firm stack.
As illustrated in the top view of Figure 1, an efficient construction uses a polarizing magnet and an AC coil that surrounds the nickel stack. When the electrical signal frequency fed to the coil corresponds to the resonant frequency of the stack, a large amount of amplitude will develop, and a sustained ultrasonic sound will be produced from the end face of the stack.
In Figure 1, the center view displays a piezoelectric ultrasonic generator using a stack of 45° Z-cut ammonium di-hydrogen phosphate (ADP) crystals fixed together. As illustrated, electrodes from the crystal faces are attached to electrical terminals, and by applying an alternating voltage at the resonant frequency of the assembly, continuous vibrations will be created, much in the same way as the magnetostriction transducer.
As illustrated in the lower view of Figure 1, a hollow polarized ceramic tube has inner and outer electrodes. The ceramic tube may be powered in a similar way as described for the ADP crystal, and sustained vibrations may be established at the ends of the ceramic tube corresponding with its length resonant frequency.
If required, one end of the tube could be covered with a solid disk in order to expand the radiating section of the transducer, and improve the acoustic power that may be generated.
Flexurally Vibrating Transducers
Another category of vibrating structures that generate sound waves uses flexural vibrations of disks, which may have a free edge or be clamped at the periphery. A free-edge disk and a clamped disk are shown in Figure 2, indicating the negative and positive displacements of the surfaces that take place during resonant vibration.
Figure 2. Examples of electroacoustic transducers operating at flexural resonance.
A bilaminar assembly comprising of two plates of polarized ceramic is depicted in Figure 2. The assembly is arranged in such a manner that when a positive potential is applied to the application, one disk expands and the other contracts. This leads to a convex displacement toward the element that develops the expanded dimension. When the applied voltage is reversed, the displacement reverses in phase in order to set up transverse vibrations.
The basic resonant frequency of a clamped circular disk is provided by 
t = thickness of disk in inches
D = diameter of disk in inches
E = modulus of elasticity in dynes/cm2
p = density in g/cm3.
For a clamped steel or aluminum disk, the resonant frequency computed from (1) becomes
For a polarized barium titanate bilaminar assembly
And for a polarized lead zirconate- titanate structure
The resonant frequency for a free disk is around 88% of the frequency indicated for the clamped disk.
Figures 1 and 2 show some basic forms of resonant electroacoustic transducers that may be used to generate ultrasonic energy in a narrow frequency band near the vibrating structure’s resonant frequency. In applications where wideband acoustic output is required, as is necessary in a sound source for calibrating ultrasonic microphones, a traditional condenser microphone can be used as an ultrasonic loudspeaker.
As shown in Figure 3 (a), a thin stretched metallic diaphragm closely spaced from a conducting back plate is used to construct a conventional-type condenser microphone. An alternating voltage is generated when a positive dc potential is applied between the diaphragm and the back plate. This is caused by the change in the capacitance between the back plate and diaphragm when the presence of sound waves sets the diaphragm into vibration.
An aluminum or a stainless-steel membrane can be stretched to achieve a resonant frequency in the neighborhood of 10 kc/s, if the diameter of the diaphragm is approximately ½”. In such conditions, the microphone will display a flat response over the low-frequency range, and exhibit a peak near the resonant frequency.
Above the resonant frequency, the vibrating system will be mass-controlled in order for the condenser microphone to become a considerably flat sound source for the ultrasonic frequency region above 10 kc/s. Rasmussen [9a] has described smaller transducers of this type that work as microphones with undiminished sensitivity' up to 100 k/s.
Figure 3. Construction of electrostatic transducer, (a) Conventional stretched-diaphragm type, (b) “Solid dielectric” type
A typical value of dc polarizing voltage of a condenser microphone is 200 V, which means that the unit could be operated as a loud-speaker with ac voltages as high as approximately 50 V before the introduction of serious distortion.
Under such conditions, a sound pressure of a few µbars will be generated over the frequency range of 10 kc/s to 100 kc/s at a distance of one foot from the transducer. Although this represents very small acoustic power, the sound field is enough to make calibrations of ultrasonic microphones.
A modification of the condenser microphone where the spaced stretched metallic diaphragm is substituted by a thin plastic film with a metalized coating on the outside surface, is shown in Figure 3(b). The film is placed in a mechanical contact with the backing plate, which results in an efficient resonant frequency of many hundred kc/s with a corresponding flat response over a wide ultrasonic-frequency area.
Plastic films of polyethylene or vinyl with a thickness of about 0.0005” were used by Kuhl, Schodder, and Schröder  to produce microphones that have resonant frequencies as high as 200 kc/s.
Wright  performed a detailed study of electrostatic transducers using metalized 0.00025 inch Mylar plastic films in direct contact with the back electrode. He revealed that even for a polished electrode surface above which the Mylar was stretched, the resultant air film with a thickness of 1 µm was responsible for the compliance, which established a resonant frequency of about 500 kc/s for the vibrating system.
The effective air gap would be larger and the resonant frequency of the system would be lower if the surface of the backing plate is rougher.
Wright obtained sensitivities ranging from - 85 dB to - 95 dB vs. 1 V/µbar for diaphragms of approximately ½ inch diameter. With these microphones, reasonably smooth wide-range ultrasonic loudspeakers can be made. These loudspeakers are limited to very low power output by the intrinsic limitations of the infinitesimal displacements that can be allowed by the design.
The inherent characteristic of the “solid dielectric” electrostatic transducer, where the sensitivity relies on the effective air gap existing between the two contacting surfaces, makes it difficult to produce a device whose sensitivity can be accurately predicted in advance.
The design also leads to a degree of variation in characteristics, making calibration of the unit essential where accurate measurements are needed.
Introducing distortion at high sound-pressure levels is a general limitation of condenser-type microphones. Distortion is important when the movement of the diaphragm plays a significant part in the effective air-gap spacing in the structure.
Standard Microphone for Ultrasonic Measurements
The characteristics of standard microphones are very stable. Their linearity allows the measurement of sound pressures of the order of several hundred lbs/in2. They use a tiny stack of ADP crystals similar to the center illustration in Figure 1.
Figure 4 displays a photograph a commercial type of such a measurement standard, together with its response characteristic. Microphones using ADP plates show very high stability.
Figure 4. Photograph and frequency responce of commercially available reference standard ADP microphone for making accurate measurements of sound pressure over very large dynamic ranges.
Many ADP transducers have been widely used for more than 15 years without any noticeable changes in their calibration. Another important advantage of this type of microphone is that it has a virtually infinite acoustic impedance, enabling accurate calibrations of intense sound fields over very wide dynamic ranges. The engineering design principles for this kind of microphone is comprehensively discussed elsewhere , .
 H. F. Olson and F. Massa, Applied Acoustics, 2nd ed. Philadelphia, Pa.: Blakiston, 1939, sect. 1.7.
 V. O. Knudsen, J. Acoust. Soc. Am., vol. 5, p. 112, October 1933.
 G. G. Stokes, Trans. Am. Phil. Soc., vol. 8, p. 287, 1845.
 L. J. Sivian, J. Acoust. Soc. Am., vol. 19, p. 914, September 1947.
 H. F. Olson and F. Massa, ob. cit., ch. 2.
 A. L. Thuras, R. T. Jenkins, and H. T. O’.N'eil, J. Acoust. Soc. Am., vol. 6, p. 173, January 1935.
 J. Hartmann, J. Sei. Instr., vol. 16, p. 141, May 1939.
 C. H. Allen and I. Rudnik, J. Acoust. Soc. Am., vol. 19, p. 857, September 1947.
 P. M. Morse, Vibration and Sound. New York: McGraw-Hill, 1936, p. 173.
[9a] G. Rasmus.sen, 1962 Proc. 4th Internat'l Congress on Acoustics, paper N51; reissued in Brüel and Kjaer Technical Review No. 1, p. 3, 1963.
 W. K. Kuhl, G. R. Schodder, and F.-K. Schröder, Acoustica, vol. 4. p. 519, 1954.
 W. M. Wright, 1962 IRE Nat’l Conv. Rec., vol. 10, pt. 6, p. 95.
 F. Massa, J. Acoust. Soc. Am., vol. 17, p. 29, July 1945.
 —, J. Acoust. Soc. Am., vol. 20, p. 451, July 1948.
 —, Electronics, p. 128, May 1960.
 —, 1960 IRE Nat’l Conv. Rec., vol. 8, pt. 6, p. 243.
This information has been sourced, reviewed and adapted from materials provided by Massa Products Corp.
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