Basic models of Ultrasonic Generators for use in Air

Table of Contents

Introduction
Modulated Air-Flow Transducers
Mechanical Vibrating Sources

Introduction

The simplest and earliest forms of ultrasonic generators convert mechanical energy directly into sound energy. Mechanical generators can be classified into two general types - the first type operates by the conversion of a stream of air into high-frequency modulated oscillation, and the second type operates by a resonant mechanical rod or plate being set into mechanical vibration.

Modulated Air-Flow Transducers

The Galton whistle (Figure 1) is one of the earliest types of ultrasonic generators, in which air travels through a nozzle that has an annular slit. The circular stream of air that travels through the slit strikes against the circular knife edge of the adjustable resonant cavity, which is developed by the adjustable plug and the hollow tube.

The resonant frequency of the cavity is determined by the position of the plug within the tube. This resonant frequency, in turn, determines the whistle’s frequency. The transducer is very simple and can be operated by blowing with the mouth. It also helps to generate frequencies as high as 100 kc/s, however the generated acoustic power is quite small.

Figure 1. Construction of Galton ultrasonic whistle

The Hartmann generator [7] shown in Figure 2, is an improvement on the Galton whistle as it allows higher acoustic powers to a certain extent. An external jet stream is generated when air is passed through the nozzle at a gauge pressure of about 0.9 atmosphere.

This jet stream will be generated beyond the nozzle tip, which will have a pressure distribution as depicted in the graph above the transducer’s cross-sectional view. As indicated by the arrows, the region of pressure rise outside of the nozzle is unstable, and a hollow body positioned in this unstable region oscillates at the cavity’s resonant frequency.

The Hartmann generator could be used to generate ultrasonic sound up to almost 100 kc/s with a conversion efficiency of the order of 5%. The Hartmann generator is considered to be a relatively low-power ultrasonic-sound source, even though the acoustic power generated by this transducer can be slightly greater than the power generated by the Galton whistle.

Figure 2. Construction of Hartmann ultrasonic generator.

A siren can be used to generate relatively high ultrasonic power in the range of several hundred watts. Allen and Rudnik [8] described a siren containing 100 conically-shaped ports closely spaced on a 6-inch diameter circle. Each port opening measures 12" long and has a diameter equal to 0.094" and 0.188" at the small end and the large end, respectively.

Figure 3 shows a schematic cross-sectional view of the siren. A high-speed motor powers a circular rotor with 100 teeth slightly wider than the port openings

At a motor speed of 18000 rpm, a 30-kc/s sound signal is produced equal to almost 200 W. In the chamber, the air pressure is about 0.2 atmosphere gauge. A siren, much like the unit shown in Figure 3, with chamber pressures increased to almost 2 atmospheres, generated acoustic outputs up to about 2 kW with a conversion efficiency of 20%.

Figure 3. Construction of an ultrasonic siren

Mechanical Vibrating Sources

A simple ultrasonic mechanical generator may comprise of a flexurally vibrating plate, a longitudinally vibrating rod, or a small timing fork, any of which could be set into vibration by hitting with a mechanical blow. The maximum amount of sound energy produced from these vibrating systems is restricted by the maximum stress which can be safely developed in the material.

Figure 4 shows a cylindrical rod of length L, which develops a peak displacement d at each end, when set into vibration at its basic resonant frequency.

Figure 4. Vibrating rod at longitudinal resonance.

The developed peak stress in the rod is given by

(1)

where

d = peak displacement in inches
E = modulus of elasticity in psi
L = length of rod in inches

For longitudinal resonance of the rod

(2)

where

c = velocity of sound in the material in in/s
f = frequency in c/s.

The velocity of sound in aluminum, nickel, and steel is roughly the same, and is equal to approximately 200 000 in/s, which, when substituted into (2), indicates that a one-inch length rod of either of these materials will have a natural resonant frequency in the neighborhood of 100 kc/s.

The fatigue limit restricts the maximum stress that can be developed in the vibrating material, and this fatigue limit is determined by the elastic limit of the material and is also considerably dependent upon the heat treatment and surface finish.

As a practical fatigue limit, a maximum safe-working stress which may be accomplished, using the best steel alloys heat treated for optimum fatigue, is approximately 30 000 psi. For a 1-inch length steel rod, the peak displacement d that can be achieved at 30 000-psi peak stress, as determined from (1), is equal to 0.0005”.

For this magnitude of peak displacement at 100 kc/s, which is the rod’s resonant frequency, Figure 1 illustrates that the acoustic power radiated from each end of the rod is about 9 W/in2 of area. If the rod is 38” diameter, the highest acoustic power that can be produced is in the vicinity of 1 W.

If a resonant rod is used as an ultrasonic generator only transient pulses can be produced if mechanical excitation is used. For remote control applications, it is possible to use a single pulse to begin the operation of a remotely located device.

For such applications, a simple ultrasonic source can be used as a resonant metallic rod, suspended at its midpoint, with a mechanically actuated striker that could be used to impart a blow to one end of the rod. However, some form of electromechanical excitation of the vibrating element can be used if sustained acoustic signals are needed.

References

[1] H. F. Olson and F. Massa, Applied Acoustics, 2nd ed. Philadelphia, Pa.: Blakiston, 1939, sect. 1.7.

[2] V. O. Knudsen, J. Acoust. Soc. Am., vol. 5, p. 112, October 1933.

[3] G. G. Stokes, Trans. Am. Phil. Soc., vol. 8, p. 287, 1845.

[4] L. J. Sivian, J. Acoust. Soc. Am., vol. 19, p. 914, September 1947.

[5] H. F. Olson and F. Massa, ob. cit., ch. 2.

[6] A. L. Thuras, R. T. Jenkins, and H. T. O’.N'eil, J. Acoust. Soc. Am., vol. 6, p. 173, January 1935.

[7] J. Hartmann, J. Sei. Instr., vol. 16, p. 141, May 1939.

[8] C. H. Allen and I. Rudnik, J. Acoust. Soc. Am., vol. 19, p. 857, September 1947.

[9] 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.

[10] W. K. Kuhl, G. R. Schodder, and F.-K. Schröder, Acoustica, vol. 4. p. 519, 1954.

[11 W. M. Wright, 1962 IRE Nat’l Conv. Rec., vol. 10, pt. 6, p. 95.

[12] F. Massa, J. Acoust. Soc. Am., vol. 17, p. 29, July 1945.

[13] —, J. Acoust. Soc. Am., vol. 20, p. 451, July 1948.

[14] —, Electronics, p. 128, May 1960.

[15] —, 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.

For more information on this source, please visit Massa Products Corp.

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