FUNDAMENTALS OF ELECTROACOUSTICS

HISTORY

Acoustics is the study of sound. Until the 19th century, acoustics primarily consisted of the physics of sound propagation related to human hearing. During the early 1800's, electromagnetics was discovered and one of the first non-musical instrument sound generators, the telegraph, was developed. The invention of the telephone in 1876 resulted in the creation of microphones and loudspeakers, followed by the phonograph at the end of the 19th century. Radio was developed during the early 1900's.

During the early part of the 20th century, a small group of researchers began applying engineering principles, such as equivalent circuits, to the science of acoustics in order to improve the design and construction of microphones and loudspeakers. This was the birth of the applied science of electroacoustics. The work was carried out in several universities and in the research laboratories of companies such as Bell Laboratories and Victor Talking Machine, which became RCA Victor.

To better communicate and share their discoveries, they formed the Acoustical Society of America in 1929, and the first text book on electroacoustics, Applied Acoustics, was authored by Frank Massa and Harry Olson in 1934. Many of the fundamental principles developed by these pioneers is still used today in the design of electroacoustic transducers and systems.

For more information on some of these early developments in electroacoustics, request from the Massa Sales Department a copy of the paper by Frank Massa entitled "Some Personal Recollections Of Early Experiences On The New Frontier of Electroacoustics During The 1920's And 1930's". The invited paper was presented at the 106th meeting of the Acoustical Society of America in San Diego on November 10, 1983, and published in the April 1985 (Vol. 77, No. 4) Journal of the Acoustical Society of America.

ACOUSTIC TRANSMISSION MEDIA

Electroacoustic transducers operate as transmitters or receivers. When operating as transmitters, they transform electrical energy into acoustic energy that propagates through a medium, which is usually air or water. When operating as receivers, they transform the acoustical energy into electrical energy.

The fundamental equations for defining sound transmission are the same for all transmission media. However, because many of the fundamental acoustical properties are vastly different between fluid media such as water and gaseous media such as air, there are many fundamental differences between transducers and systems that are designed to operate in them. Massa is one of the few organizations that design and manufacture electroacoustic transducers and systems for both underwater (sonar) applications and specialized industrial ultrasonic application in air. Some comparative acoustic properties of air and water are contained in Table I.

TABLE I

Temp.(C)Density(kg/m3)Velocity(m/sec.)Acoustic Impedance(MKS Rayls)

Fresh Water20 1000 1480 1.48 x 106

Sea Water (35 ppt salinity)13 1026 1500 1.54 x 106

Air0 1.29 332 428

Air20 1.21 343 415

GENERAL PROPERTIES

Wavelength of Sound as a Function of Sound Speed and Frequency

The wavelength of sound changes as a function of both speed of sound and frequency, as shown by the expression:

Figure 1 shows a plot of the wavelength of sound from Equation (1) in air and water at room temperature as a function of frequency.

Figure 1Plot of the Wavelength as a Function of Frequencyfor Sound in Air and Water at Room Temperature

Transducer Beam Patterns

The acoustic radiation pattern, or beam pattern, is the relative sensitivity of a transducer as a function of spatial angle. This pattern is determined by factors such as the frequency of operation and the size, shape and acoustic phase characteristics of the vibrating surface. The beam patterns of transducers are reciprocal, which means that the beam will be the same whether the transducer is used as a transmitter or as a receiver. It is important to note that the system beam pattern is not the same as the transmitting or receiving beam pattern of the transducers, as will be explained in a later section.

Transducers can be designed to radiate sound in many different types of patterns, from omnidirectional to very narrow beams. For a transducer with a circular radiating surface vibrating in phase, as is most commonly used in ultrasonic sensor applications, the narrowness of the beam pattern is a function of the ratio of the diameter of the radiating surface to the wavelength of sound at the operating frequency. The larger the diameter of the transducer as compared to a wavelength of sound, the narrower the sound beam. Figure 2 Three-Dimensional Representation of the Beam Pattern Produced bya Transducer With a Diameter Large Compared to a Wavelength

As can be seen, it produces a narrow conical beam and a number of secondary lobes of reduced amplitude separated by nulls. Even though the beam is called conical, it does not have straight sides and a flat top as the word "conical" may imply. The beam angle is usually defined as the measurement of the total angle where the sound pressure level of the main beam has been reduced by 3 dB on both sides of the on-axis peak. However, the transducer still has the sensitivity at greater angles, both in the main beam and in the secondary lobes.

When describing the beam patterns of transducers, two-dimensional plots are most commonly used. They show the relative sensitivity of the transducer vs. angle in a single plane cut through the three-dimensional beam pattern. For a symmetrical conical pattern, such as that shown in Figure 2, a simple two-dimensional plot will describe the entire three-dimensional pattern. Figure 3 shows a two-dimensional polar plot from -90 to +90 of the beam of a circular radiating piston mounted in an infinite baffle with a diameter equal to two wavelengths of sound. As can be seen, the pattern is smooth as a function of angle, and the -3 dB points are at +15 and -15 off axis, producing a total beam angle of 30. However, the total angle of the major radiating lobe between the first two nulls is approximately 70, and the side lobes peak at approximately +55 and -55.

Figure 3A Two Dimensional Polar Plot is Shown Which Representsthe Beam Pattern of a Transducer Mounted in an Infinite BaffleWith a Circular Disk Radiatior (Diameter/Wavelength = 2)

When using transducers, it is important to be aware that nearby unwanted targets that are beyond the beam angle can inadvertently be detected, because the transducers are still sensitive at angles greater than the beam angle. Some transducers used in sensing applications are specially designed to minimize or eliminate the secondary lobes to avoid detecting unwanted targets.

System Beam Patterns

In the operation of an echo ranging system, the transmitting transducer sends out sound at reduced amplitudes at different angles, as described by the beam pattern of the transmitting transducer. The receiving transducer has less sensitivity to echoes received at angles off axis, as described by the beam pattern of the receiving transducer. The system beam pattern is the sum in dB of beam patterns of the transmitter and the receiver.

The solid curve of Figure 4 shows a plot of the beam pattern of Figure 3 on rectilinear coordinates for angles from 0 to 30 off axis. This beam pattern is the same for the transducer whether it is transmitting or receiving. The dotted curve shows the system beam pattern when the transmitting transducer and receiving transducer each have the same beam shown by the solid curve. As can be seen, the system beam pattern is narrower then the pattern of the transducer alone.

Figure 4The Transducer Beam Pattern of Figure 3 is Plotted onRectilinear Coordinates as the Solid Curve, and the SystemBeam Pattern for a Sensor Using the Tranducer to BothTransmit and Receive is Plotted as the Dotted Curve

ULTRASONIC TRANSDUCERS AND SYSTEMS OPERATING IN A GASEOUS MEDIUM

Ultrasonic sound is a vibration at a frequency above the range of human hearing, usually greater than 20 kHz. The microphones and loudspeakers used to receive and transmit ultrasonic sound are called transducers. Most ultrasonic sensors are echo ranging systems that use a single transducer to both transmit the sound pulse and receive the reflected echo, typically operating at frequencies between 40 kHz and 250 kHz. A variety of different types of transducers can be used in these systems. For a more detailed discussions of this subject, request from the Massa Sales Department a reprint of the two-part article by Donald P. Massa entitled "Choosing An Ultrasonic Sensor For Proximity Or Distance Measurement; Part 1: Acoustic Considerations; Part 2: Optimizing Sensor Selection" that was published in the February and March 1999 editions of Sensors.

Speed of Sound in Air as a Function of Temperature

The speed of sound in air varies as a function of temperature by the relationship:

(2)

Attenuation of Ultrasonic Sound in Air as a Function of Frequency and Humidity

As the sound travels, the amplitude of the sound pressure is reduced due to friction losses in the transmission medium. The attenuation of sound in air increases as the frequency increases, and at any given frequency the attenuation varies as a function of humidity. The value of humidity that produces the maximum attenuation is not the same for all frequencies. For example, above 125 kHz the maximum attenuation occurs at 100% relative humidity; however, at 40 kHz the maximum attenuation occurs at 50% relative humidity.

Since an ultrasonic sensor usually is required to operate at all possible humidities, target range calculations should use the largest value of attenuation. A good estimate for the maximum attenuation in air at room temperature over all humidities for frequencies up to 50 kHz is given by:

(3a)

For frequencies between 50 kHz and 300 kHz, the maximum attenuation over all humidities is:

(3b)

Figure 5 is a plot showing the maximum attenuation of sound as a function of frequency in air at room temperature over all humidities for frequencies between 40 kHz and 250 kHz. Figure 6 shows a family of curves that plot the variations in the attenuation of sound in air at room temperature as a function of humidity for various frequencies between 40 kHz and 200 kHz.

Figure 5Maximum Attenuation of Sound vs. Frequencyin Air for All Humidities

FIgure 6Attenuation of Sound in Air vs. Humidityfor Different Frequencies

INCLUDEPICTURE "http://counter2.hitslink.com/stats-ns.asp?acct=creasemonkey&v=1&s=205" \* MERGEFORMATINET Part 1: Acoustic ConsiderationsThe first step toward identifying the right proximity sensor for your application is to understand the fundamental ultrasonic properties of the transmission medium and the way they influence the measurement and system operation.Donald P. Massa, Massa Products Corp.

Ultrasonic sensors are commonly used for a wide variety of noncontact presence, proximity, or distance measuring applications. These devices typically transmit a short burst of ultrasonic sound toward a target, which reflects the sound back to the sensor. The system then measures the time for the echo to return to the sensor and computes the distance to the target using the speed of sound in the medium [1,2,3].

The wide variety of sensors currently on the market differ from one another in their mounting configurations, environmental sealing, and electronic features. Acoustically, they operate at different frequencies and have different radiation patterns. It is usually not difficult to select a sensor that best meets the environmental and mechanical requirements for a particular application, or to evaluate the electronic features available with different models. Still, many users may not be aware of the acoustic subtleties that can have major effects on ultrasonic sensor operation and the measurements being made with them.

The overall intent of this article is to help the user select an ultrasonic sensor with the best acoustical properties, such as frequency and beam pattern, for a particular application, and how to obtain an optimum measurement from the sensor. The first step in this process is to gain a better understanding of how variations in the acoustical parameters of both the environment and the target affect the operation of the sensor. Specifically, the following variables will be discussed:

Variation in the speed of sound as a function of both temperature and the composition of the transmission medium, usually air, and how these variations affect sensor measurement accuracy and resolution Variation in the wavelength of sound as a function of both sound speed and frequency, and how this affects the resolution, accuracy, minimum target size, and the minimum and maximum target distances of an ultrasonic sensor Variation in the attenuation of sound as a function of both frequency and humidity, and how this affects the maximum target distance for an ultrasonic sensor in air Variation of the amplitude of background noise as a function of frequency, and how this affects the maximum target distance and minimum target size for an ultrasonic sensor Variation in the sound radiation pattern (beam angle) of both the ultrasonic transducer and the complete sensor system, and how this affects the maximum target distance and helps eliminate extraneous targets Variation in the amplitude of the return echo as a function of the target distance, geometry, surface, and size, and how this affects the maximum target distance attainable with an ultrasonic sensor

Fundamental Ultrasonic PropertiesUltrasonic sound is a vibration at a frequency above the range of human hearing, usually >20 kHz. The microphones and loudspeakers used to receive and transmit the ultrasonic sound are called transducers. Most ultrasonic sensors use a single transducer to both transmit the sound pulse and receive the reflected echo, typically operating at frequencies between 40 kHz and 250 kHz. A variety of different types of transducers are used in these systems [4] . The following sections provide an overview of how the sound pulse is affected by some of the fundamental ultrasonic properties of the medium in which the sound travels.

Speed of Sound in Air As a Function of TemperatureIn an echo ranging system, the elapsed time between the emission of the ultrasonic pulse and its return to the receiver is measured. The range distance to the target is then computed using the speed of sound in the transmission medium, which is usually air. The accuracy of the target distance measurement is directly proportional to the accuracy of the speed of sound used in the calculation. The actual speed of sound is a function of both the composition and temperature of the medium through which the sound travels (see Figure 1).

Figure 1. The speed of sound is plotted as a function of the temperature. At room temperature, sound travels at ~13,500 ips.

The speed of sound in air varies as a function of temperature by the relationship [5]:

(1)

where:

c(T)= speed of sound in air as a function of temperature in inches per second

T= temperature of the air in C

The speed of sound in different gaseous media is a function of the bulk modulus of the gas, and is affected by both the chemical composition and temperature. Table 1 gives the speed of sound for various gases at 0C [6].

TABLE 1

Speed of Sound for Various Gases

GasSpeed, in./s at 10C

Helium38,184

Hydrogen49,980

Illuminating Gas19,308

Methane17,004

Neon17,124

Nitric Oxide12,792

Nitrogen13,152

Nitrous Oxide10,308

Oxygen12,492

Steam (100C)15,876

GasSpeed, in./s at 10C

Air13,044

Ammonia16,332

Argon11,886

Carbon Dioxide10,152(low frequency)10,572(high frequency)

Carbon Disulfide7,272

Carbon Monoxide13,272

Chlorine8,088

Ethylene12,360

Wavelength of Sound As a Function of Sound Speed and FrequencyThe wavelength of sound changes as a function of both the speed of sound and the frequency, as shown by the expression:

= c/f (2)

where:

= wavelength

c= speed of light

f= frequency

Figure 2 is a plot of the wavelength of sound as a function of frequency at room temperature in air.

Figure 2. The wavelength of sound in air at room temperature is plotted as a function of frequency.

Attenuation of Sound As a Function of Frequency and HumidityAs the sound travels, the amplitude of the sound pressure is reduced due to friction losses in the transmission medium. Knowing the value of this absorption loss, or attenuation, is crucial in determining the maximum range of a sensor. The attenuation of sound in air increases with the frequency, and at any given frequency the attenuation varies as a function of humidity. The value of humidity that produces the maximum attenuation is not the same for all frequencies [7]. Above 125 kHz, for example, the maximum attenuation occurs at 100% RH; at 40 kHz, maximum attenuation occurs at 50% RH.

Since an ultrasonic sensor usually is required to operate at all possible humidities, target range calculations should use the largest value of attenuation. A good estimate for the maximum attenuation in air at room temperature over all humidities for frequencies up to 50 kHz is given by:

(f) = 0.01 f (3a)

where:

(f)= maximum attenuation in dB/ft

f= frequency of sound in kHz

Between 50 kHz and 300 kHz, the maximum attenuation over all humidities is:

(f) = 0.022 f 0.6 (3b)

Figure 3 and Figure 4 illustrate the attenuation of sound as a function of frequency and humidity.

Figure 3. The maximum attenuation of sound in air at room temperature can be plotted as a function of frequency over all humidities for frequencies between 40 kHz and 250 kHz.

Figure 4. This family of curves shows the variations in the attenuation of sound in air at room temperature as a function of humidity for frequencies between 40 kHz and 200 kHz.

Background NoiseThe level of background ultrasonic noise diminishes as the frequency increases. The reason is that less noise at the higher frequencies is produced in the environment, and the noise that is produced is greatly attenuated as it travels through the air.

Effects of Frequency, Distance, and the TransmissionMedium on the Magnitude of Sound PressureIn an ultrasonic sensor, the transducer produces a short pulse of sound. The magnitude of the sound pressure generated will vary from one type of sensor to another. In acoustics, sound pressures are typically expressed in decibels because of their large dynamic ranges. Sound pressure is usually measured in micropascals (Pa) at a reference distance, R0, from the sensor, usually 12 in. (30 cm). The sound pressure level (SPL) at R0 is then converted to dB referenced to (//) 1Pa as follows:

SPL(R0) = 20 log(p) (4)

where:

SPL(R0)= sound pressure level at distance R0 in dB//1Pa

p= sound pressure at distance R0 in Pa

As the sound travels through the medium, the magnitude of the sound pressure is reduced due to both absorption (attenuation) and spreading loss caused by the expanding surface of the radiating beam as the sound pulse travels from the transducer. The SPL at a distance R from the transducer is given by:

SPL(R) = SPL(R0) 20 log (R/R0) (f) R (5)

where:

SPL(R)= sound pressure level at distance R in dB//1Pa

SPL(R0)= sound pressure level at distance R0 in dB//1Pa

(f)= attenuation coefficient in dB/unit distance at frequency f

Relative Echo Levels From a Flat Surface forDifferent Ultrasonic FrequenciesFigure 5. A sound beam reflected from a flat surface is equivalent to the sound as generated from a virtual transducer at an equal range behind the reflecting plate.

If the sound pulse is reflected from a large flat surface, then the entire beam is reflected (see Figure 5). This total beam reflection is equivalent to a virtual source at twice the distance. Therefore, the spreading loss for the sound reflected from a large flat surface is equal to 20 log (2R), and the absorption loss is equal to 2 R. For this to hold, it is important that the reflecting surface be both larger than the entire sound beam to ensure total reflection, and perpendicular to the sound beam.

Equation (5) can be used to compute the relative effect of varying the sound frequency on echoes produced from a flat reflector at different distances from the sensor. In Figure 6, it is assumed that each sensor produced the same SPL at a range of 1 ft.

Figure 6. The relative echo levels from a flat reflecting target at varying distances are plotted against range for different frequencies.

Therefore, the variations in EL are only a function of the varying attenuations due to the different frequencies of sound. The maximum attenuation for all humidities was used for the value of for each frequency.

SummaryPart 1 of this article has provided an overview of the some of the fundamental acoustical parameters that affect the operation of an ultrasonic sensor. Part 2 will address the use of these acoustical data to optimize the selection of an ultrasonic sensor for a particular measurement.

References1. Frank Massa. May 1992. "Ultrasonics in Industry," Fiftieth Anniversary Issue, Proc IRE.

2. Donald P. Massa. Oct. 1987. "An Automatic Ultrasonic Bowling Scoring System," Sensors, Vol. 4, No. 10.

3. Paul A. Shirley. Nov. 1989. "An Introduction to Ultrasonic Sensing," Sensors, Vol. 6, No. 11.

4. Frank Massa. Oct. 1965. "Ultrasonic Transducers for Use in Air," Proc IEEE, Vol. 53, No. 10.

5. Leo L. Beranek. 1972. "Acoustic Properties of Gases," American Institute of Physics Handbook, 3rd Ed. (Section 3d), McGraw-Hill.

6. Handbook of Chemistry and Physics, 45th Ed., 1964.

7. L.B. Evans and Bass. Jan. 1972. "Tables of Absorption and Velocity of Sound in Still Air at 68F," Wyle Laboratories, Report WR72-2.

Choosing an Ultrasonic Sensor forProximity or Distance Measurement An understanding of radiation patterns and the target's effect on echoes is essential to evaluating candidate sensors in terms of frequency variations, accuracy and resolution, target range, effective beam angle, and the influence of ambient temperature variations on sensor performance.Donald P. Massa, Massa Products Corp.

Part 1 of this article, which appeared in the February issue of Sensors, was an overview of some of the fundamental acoustical parameters that affect the performance of an ultrasonic sensor. In Part 2 we address radiation patterns and echo variation from targets other than flat surfaces, and the way these parameters can be used to help optimize the selection and operation of ultrasonic sensors for different applications. The figures, equations, and references are numbered sequentially from Part 1.

Radiation Patterns of Transducers and Ultrasonic SensorsTransducer Beam Patterns. The acoustic radiation pattern, or beam pattern, is the relative sensitivity of a transducer as a function of spatial angle. This pattern is determined by factors such as the frequency of operation and the size, shape, and acoustic phase characteristics of the vibrating surface. The beam patterns of transducers are reciprocal, which means that the beam will be the same whether the transducer is used as a transmitter or as a receiver. It is important to note that the system beam pattern of an ultrasonic sensor is not the same as the beam pattern of its transducer, as will be explained later.

Transducers can be designed to radiate sound in many different types of pattern, from omnidirectional to very narrow beams. For a transducer with a circular radiating surface vibrating in phase, as is most commonly used in ultrasonic sensor applications,

Figure 7.A transducer with a circular radiating surface whose diameter is large in comparison to a wavelength produces a narrow, conical beam pattern with multiple secondary lobes.

the narrowness of the beam pattern is a function of the ratio of the diameter of the radiating surface to the wavelength of sound at the operating frequency, D/[8]. The larger the diameter of the transducer as compared to a wavelength of sound, the narrower the sound beam. For example, if the diameter is twice the wavelength, the total beam angle will be ~30, but if the diameter or frequency is increased so that the ratio becomes 10, the total beam angle will be reduced to ~6.

For most ultrasonic sensor applications, it is desirable to have a relatively narrow beam pattern to avoid unwanted reflections. The diameter of the transducers is therefore usually large compared to a wavelength.

Figure 7 is a 3D representation of the beam pattern produced by a transducer with a diameter that is large compared to a wavelength. As can be seen, the beam is narrow and conical and has a number of secondary lobes separated by nulls. Each of these secondary lobes is sequentially lower in amplitude than the previous one. (Even though the beam is called conical, it does not have straight sides and a flat top as the word might imply.) The beam angle is usually defined as the measurement of the total angle where the sound pressure level of the main beam

Figure 8.Chart No. 67 from Acoustic Design Charts shows the directional radiation characteristic of circular pistons mounted in an infinite baffle as a function of D/.

has been reduced by 3 dB on both sides of the on-axis peak. However, the transducer still has sensitivity at greater angles, both in the main beam and in the secondary lobes [9]. Figure 8 (page 28) is a family of curves reproduced from Acoustic Design Charts for transducers with circular radiating pistons mounted in an infinite baffle. The curves show the degrees off axis for the beam angle to be reduced from the on-axis amplitude by 3 dB, 6 dB, 10 dB, and

20 dB as a function of D/ [10]. Note that the angles on these curves are half of the total beam angle.

When describing transducer beam patterns, 2D plots are most commonly used. These show the relative sensitivity of the transducer vs. angle in a single plane cut through the 3D beam pattern. For a symmetrical conical pattern such as that shown in Figure 7, a simple 2D plot will describe the entire 3D pattern. Figure 9 shows a 2D polar plot

Figure 9.This 2D polar plot represents the beam pattern of a transducer with a circular disc radiator mounted in an infinite baffle, where D/ = 2.

from 90 to +90 of the beam of a circular radiating piston mounted in an infinite baffle with a diameter equal to two wavelengths of sound. As can be seen, the pattern is smooth as a function of angle, and the 3 dB points are at +15 and 15 off axis, producing a total beam angle of 30. However, the total angle of the major radiating lobe between the first two nulls is ~70, and the side lobes peak at approximately +55 and 55. When using an ultrasonic sensor, it is important to be aware that nearby unwanted targets that are beyond the beam angle can inadvertently be detected because the transducers are still sensitive at angles greater than the beam angle. Some transducers used in sensing applications are specially designed to minimize or eliminate the secondary lobes to avoid detecting unwanted targets.

System Beam Patterns. In an echo ranging system, the transmitting transducer sends out sound at reduced amplitudes at different angles, as described by the beam pattern of the transmitting transducer. The receiving transducer has less sensitivity to echoes received at angles off axis, as described by the beam pattern of the receiving transducer. The system beam pattern is the sum in decibels of the transmitter's and the receiver's beam patterns.

The solid curve of Figure 10 (page 32) is a plot of the beam pattern of Figure 9 on rectilinear coordinates for angles from 0 to 30 off axis. This beam pattern is the same for the transducer whether it is transmitting or receiving. The dashed curve shows the system beam pattern for a sensor using this same transducer to both transmit and receive. As can be seen, the system beam pattern for the ultrasonic sensor is narrower than the pattern of the transducer alone.

Figure 10.The transducer beam pattern of Figure 9 is plotted on rectilinear coordinates as the solid curve, and the system beam pattern for a sensor using the transducer to both transmit and receive is plotted as the dashed curve.

A target located on the acoustic axis ( = 0) will produce an echo that is not reduced in amplitude due to the transmitting beam pattern, and the voltage the echo will cause the receiving transducer to produce will not be diminished due to its beam pattern. If a target is 15 off axis, however, the sound pulse from the transmitter will be reduced by 3 dB due to the beam pattern, which will cause the magnitude of the resulting echo to be reduced by 3 dB. When the echo reaches the receiver, the resulting voltage produced will be reduced by another 3 dB from the voltage that the same magnitude of echo would have produced if it had been received on the acoustic axis of the transducer. Therefore, the 3 dB reduction in echo level plus the 3 dB reduction in receive sensitivity result in a total reduction of 6 dB in the voltage produced by a target 15 off axis as compared to the same target located directly on the acoustic axis.

The magnitude of the voltage in the system produced by a target echo as a function of angle will therefore be reduced by twice the number of decibels as indicated by the beam pattern of the transducer alone, if the same transducer is used to both transmit and receive. Since this difference can obviously have a significant effect on ultrasonic sensor operation, system beam patterns, not transducer beam patterns, should be used when evaluating a sensor application.

Targets' Effect on EchoesThe relative echo levels from large flat surfaces where the reflector is larger than the entire incident sound beam was discussed in Part 1 of this article. This type of reflection is typical for an ultrasonic sensor used in applications such as liquid level control. For other types or sizes of targets, though, the echo levels are affected differently. Figure 11 (page 33) illustrates the behavior of a small sphere as a target. As can be seen, the sphere intercepts only a portion of the sound beam and then reradiates the sound pulse. During this process, the sound pressure is reduced by spreading loss, 20 log (R/R0), as it travels from the sensor to the target. When the sound reradiates from the target, the sound pressure is again reduced by spreading loss as it travels back toward the sensor.

Figure 11. A small sphere used as a target partially reflects the beam and reradiates an echo.

In the case of a reradiating target, the total spreading loss will therefore be 40 log (R/R0), which is the sum of the spreading loss for the sound traveling to the target plus the spreading loss of the reradiated sound returning to the sensor.

The measure of the reflectivity of a target is called Target Strength (TS) [11]. It is defined as 10 the logarithm to the base 10 of the intensity of the sound returned by a target at a reference distance from its "acoustic center," divided by the incident intensity of the transmitted sound pulse. The TSs of simple geometric shapes can be theoretically computed; Table 2 contains the expressions of TS for a few types of target forms. When using this table, all dimensional units must be the same, including the reference range, R0, the range distance to the target, R, and all dimensions of the targets.

Such idealized computations of TS should be used only as approximations of real targets, since actual targets are usually not simple reflectors but rather are complex with multiple surfaces of reflection. The sound reflecting from each of these multiple surfaces will produce echoes of different amplitudes that will sum together when they return to the sensor. Since the sound pulse is reflected at different times by the various reflecting surfaces as it propagates across the target, the individual echoes will be different in both amplitude and phase. The total received echo will therefore be a complex summation of these multiple pressure waves of different amplitudes and phases.

Any movement of the target, or any variation in the relative velocity of sound due to air turbulence along the various acoustic path lengths from the different reflecting surfaces of the target, will cause a dramatic change in the TS. The result can be large variations in the echo level produced by a target from one pulse to another during ultrasonic sensor operation. The extent of the variations in TS for a specific target in a given environment can be experimentally determined by measuring the changes in the magnitudes of echoes from the target for a series of pulses at all expected variations of target position and over all expected environmental conditions.

For reradiating targets, the echo level as a function of target range is:

ELf (R) = SPL(R0) 40 log (R/R0)

2fR + TS (6)

where:

ELf (R) = echo level at frequency f

R = range distance to target

SPL(R0) = sound pressure level of

transmitter at reference

distance R0f = attenuation coefficient of sound

at frequency f

TS =target strength

Equation (6) can be used to compute the relative effect that varying the sound frequency will have on echoes produced from reradiating targets at different distances from the sensor. For example, it is assumed that the same sound pressure level is produced by the sensor at all frequencies, and that the same target is placed in line with the acoustic axis of the transducer. For illustration, the target is assumed to be a sphere with a radius equal to 6 in. (1/2 ft). From Table 2, this will result in a TS equal to

12 dB. Figure 12 shows plots of the relative ELf (R) from a reflecting sphere with a 6 in. radius at different distances from sensors operating at different frequencies.

Comparing Figure 12 to Figure 6 in Part 1 shows that there is a considerable reduction in level when an echo from a large flat reflector is compared to an echo from a 6-in.-radius sphere at the same range and frequency. This shows that the maximum range of a sensor can be greatly reduced by different targets.

Selecting and Using Ultrasonic SensorsWhen selecting an ultrasonic sensor for a particular application, it is important to consider how the echo will be affected by the acoustical fundamentals. There is a wide variety of sensors available that operate at different frequencies and have different beam angles. In addition, systems can have different electronics options such as temperature sensing and signal averaging. The proper choice of sensor parameters will help optimize the system performance.

Variations in Frequency of Sensors. In general, the lower the frequency of the sensor, the longer the range of detection, while a higher frequency sensor will have greater measurement resolution and less susceptibility to

Figure 12. The relative echo levels from a 6-in.-radius sphere at varying distances are plotted against range for different frequencies.

background noise. The background noise produced under most conditions is lower in amplitude at higher frequencies, and will attenuate more at higher frequencies as it travels toward the sensor. Because most sensors produce relatively narrow beam angles, the physical size of the transducer in the sensors will typically become larger as the frequency decreases.

Absolute Accuracy, Relative Accuracy, and Resolution. The concepts of absolute accuracy, relative accuracy, and resolution are different in ultrasonic sensors. Absolute accuracy is the uncertainty error in the exact distance measurement from the face of the ultrasonic sensor to the target. Relative accuracy is the uncertainty error in the change in distance measurement when the target moves relative to the sensor. Resolution is the minimum change in distance that can be measured by the sensor when the target moves relative to it. These measurements are affected by factors such as the wavelength of the sound, the Q of the transducer, the reflecting characteristics of the target, the operation of the target detection electronics in the sensor, and the uncertainty in the assumed value of the speed of sound.

Uncertainty in accurately knowing the exact speed of sound over the entire transmission path is usually the major contribution to inaccuracy in the absolute measurement of the range to the target. Figure 1 in Part 1 shows the speed of sound in air as a function of temperature based on Equation

Figure 13. The uncertainty errors in inches are plotted for different absolute range measurements for a 1C uncertainty in temperature. The solid curve is used if range R is in feet; the dashed curve is used if R is in inches.

1). During operation, the ultrasonic sensor measures the time interval from when the sound pulse is transmitted to when the echo is received, t, and computes the target range.

In the vicinity of room temperature, a 1C change in temperature will produce an uncertainty in sound speed of ~23 ips. This causes an uncertainty error in the accuracy of the absolute distance measurement for a 1C temperature change of:

errRin(R) = 0.0017 R (7a)

errRft(R) = 0.0204 R (7b)

where:

errRin(R) = uncertainty error in target range in inches for a 1C uncertainty in temperature when target range R is in inches

errRft(R) = uncertainty error in target range in inches for 1C uncertainty in temperature when target range R is in feet

Figure 13 plots the uncertainty error in the absolute target range measurement in inches as a function of target range for a 1C uncertainty in temperature, as computed by Equations (7a) and (7b). The solid curve shows the measurement error if the target range R is in feet; the dashed curve is for target range in inches.

Uncertainties in the average value of the speed of sound along the acoustic path can occur for a variety of reasons. A sensor with an internal temperature probe will obviously have less uncertainty in sound speed approximation than a sensor that does not measure the temperature. In some applications, however, the temperature in the transmission medium between sensor and target can be different from the temperature at the sensor, which therefore will cause an error even if a temperature probe is used.

If there is air turbulence along the path from the sensor to the target, then the average speed of sound will randomly change, causing the target range computed by the sensor to randomly vary from pulse to pulse. Similar variations in the arrival time of a target echo will appear if the target surface is moving, such as when a liquid surface contains waves. For these applications, measurement accuracy will increase if the sensor is capable of averaging a number of measurements before providing a target range output.

The uncertainty in sound speed over the acoustic path has much less effect on the sensor's relative accuracy when a change in target range is being measured. For this situation, equation (7a) becomes:

errRin(R) = 0.0017 R (8)

where:

errRin(R) = uncertainty error in relative change in target range in inches for a 1C uncertainty in temperature when target range changes by R inches

If the temperature is unknown by 5C, and a target at a range of 100 in. moves 0.500 in. toward the sensor, the error in the absolute target range measurement of 100 in. will be 0.85%, or 0.85 in. However, the error in the relative distance measurement of 0.500 in. will be only 0.004 in.

The resolution of a range measurement made with an ultrasonic sensor is influenced by many factors. Since the sensor is measuring the arrival time of an acoustic pulse, the higher the ultrasonic frequency the greater the resolution because both the wavelength and period of the echo signal are smaller at higher frequencies. The accuracy of the time-measuring circuits in the sensor also affects the resolution, as will the averaging capabilities of a sensor if there is turbulence along the sound path. The best way to measure the true resolution of an ultrasonic sensor for a particular application is to place a target at a fixed distance and obtain a stable range measurement. Then slowly move the target forward or backward until the sensor indicates a measurable change in target range. Accurately measure the distance the target moved. This change in distance is the resolution of the sensor. Compare the actual distance the target moved to the change in range measured by the sensor. This is the error in the resolution of the device.

Target Range Measurement. For each application, it is important to select a sensor that will detect the desired targets when they are located within a specified area in front of the sensor, but ignore all targets outside this area. As previously noted, a lower frequency sensor should be selected for longer ranges of detection and a higher frequency sensor should be used for shorter range, higher resolution measurements. Sensor beam angles should be selected to cover the desired detection geometry, and to reject unwanted targets.

The maximum range at which an ultrasonic sensor can detect a target is affected by attenuation of the sound and the target strength. These effects can be illustrated by using the data in Figure 6 in Part 1 and Figure 12, and setting a minimum echo detection threshold. Table 3 was prepared by arbitrarily choosing for illustration

Figure 14. The relative echo levels of a 100 khz sound pulse from a flat rflective target at varying distances are plotted against a range for 0% and 90% RH.

60 dB//1Pa as the minimum echo level the sensor can detect. It shows that the range at which the echo level reaches

60 dB//1Pa will vary for sensors operating at different frequencies between 40 kHz and 200 kHz for both a large flat target and a 6-in.-radius sphere. These range values are therefore the maximum detection ranges for the sensors and targets used in this illustration.

As can be seen from Table 3, the lower the sound frequency, the longer the detection range. The maximum detection range of a sensor is greatly reduced, however, when the target is spherical rather than a large flat reflector, and the percentage of range reduction is greater for lower frequencies. At 200 kHz, the maximum range between the targets is decreased by 33%, while at 40 kHz the range reduction is 67%.

Humidity can also have a significant effect on the target range. The curves of Figure 6 in Part 1 and Figure 12 use values of attenuation that are greater than the maximum attenuation that would be caused by humidity variations at each frequency. Figure 4 in Part 1 shows that there is a large variation in attenuation at any particular frequency as the humidity varies. For example, at 100 kHz the attenuation varies from 0.5 dB/ft at 0% RH to 1.3 dB/ft at 90% RH. This means that if a target is at a range of 10 ft from the sensor, the echo level will change a total of 16 dB if the humidity changes from 0% to 90%.

Figure 14 shows plots of the relative echo levels from a large flat target that can be obtained with a sensor operating at 100 kHz for humidities of 0% RH and 90% RH. As can be seen, the magnitude of the echoes at each range changes dramatically between the two humidities, so the maximum detectable range of the sensor for a given target will also be greatly affected by humidity. It is therefore possible to successfully install a sensor for a particular application, and at a later date find that it is no longer detecting targets if the humidity changed enough to cause the target echoes to attenuate below the detection threshold of the sensor.

Effective Beam Angle. It is important to consider an ultrasonic sensor's effective beam angle, which is the angle around the acoustic axis where a target will be detected. If the target moves closer to the sensor, or if a target with a greater TS is used, then the effective beam angle will increase. At only one range for a particular target will the effective beam angle be equal to the classical beam angle that is obtained from the polar radiation pattern. Therefore, the classical beam angle can be used only as a first order guide in determining whether targets will be detected or ignored by the sensor.

At the maximum detection range, the amplitude of the target echo is just barely large enough to be detected by the sensor electronics when the target is directly in line with the transducer's acoustic axis. Reducing the echo level by rotating the target slightly off the beam's acoustic axis will lower the amplitude of the echo below the sensor's detection threshold. Under these operating conditions, the effective beam angle of the sensor will therefore be essentially 0.

As a target moves closer to the sensor, the echo level increases dramatically. For a sensor operating at 100 kHz and using a large flat plate as a target, the echo level can increase more than 60 dB as the target moves from a range of 10 ft to a range of 1/2 ft. This means that at a range of 1/2 ft, for any angle off the acoustic axis where the sensor beam pattern has not reduced more than 60 dB, the flat target will produce an echo larger than that from the target on axis at a range of 10 ft. For a sensor with a transducer radiation pattern as shown in Figures 9 and 10, a large flat target at a 1/2 ft range would be detected almost continuously as the sensor is rotated 90. Some sensors have variable gain amplifiers that lower the detection levels for close targets, and therefore reduce the tendency to widen the effective beam angle of the sensor.

SummaryThis two-part article has provided a brief overview of some of the fundamentals that influence the operation of ultrasonic sensors. As was shown, the maximum detection range of an ultrasonic sensor is typically longer for lower frequencies, while the resolution and accuracy are typically better at higher frequencies. The strength of the target echo, however, is greatly affected by the geometry and reflectivity of the target, thereby affecting the range and resolution of the distance measuring system.

One of the biggest sources of error in an ultrasonic position measurement is the variability of sound speed in the transmission path between the sensor and the target, largely caused by uncertainty in the average temperature along the path. Maximum measurement accuracy is therefore obtained when temperature compensation is used within the sensor. Note that temperature uncertainty affects absolute accuracy substantially more than it does the relative accuracy of an incremental measurement.

It is not unusual for the amplitude of echo levels to change by large amounts from pulse to pulse due to variations in sound speed in the medium, caused by factors such as air turbulence or target movement. Also, long-term changes in humidity can have a significant effect on the strength of an echo from a target.

It is usually desirable to use a sensor with the narrowest possible radiation pattern that can detect the required targets. For a greater frequency, the narrower the radiation pattern of the sensor, the longer the maximum range of the sensor and the less susceptibility to unwanted targets at the sides of the sensor. However, a very narrow radiation pattern from a sensor will require more accurate orientation of the sensor's axis with regard to the acoustic beam's perpendicularity to a flat target. In any event, the user must understand the effective beam angle of the sensor when determining which targets will be detected and which will be ignored. This effective beam angle changes with the distance of the target and the strength of the reflection from the target.

References8. Leo L. Beranek. 1954. Acoustics, McGraw-Hill:91-106.

9. Introduction to Sonar Technology. 1965. Bureau of Ships, Dept. of the Navy, NAVSHIPS 0967-129-3010.

10. Frank Massa. 1942. Acoustic Design Charts, The Blakiston Company:141.

11. Robert J. Urick. Principles of Underwater Sound (3rd Ed.), McGraw-Hill:291-308.

A successful application of an ultrasonic distance measurement system takes into account the operating principles of the apparatus, environmental factors, and characteristics of the target.An Introduction to Ultrasonic Sensing

Paul A. Shirley, Massa Products Corp.

UItrasonic ranging and detecting devices use high-frequency sound waves to detect the presence of an object and its range. The systems either measure the echo reflection of the sound from objects or detect the interruption of the sound beam as the objects pass between the transmitter and receiver.

Transducer Configurations

A transmitting transducer sends out a pulse of sound that is detected by a receiving transducer. Figure 1 shows several types of transducer configurations. In Figure 1(A), two transducers are mounted side by side. In this application, ultrasonic energy from the transmitter is reflected by an object and the echo is detected by the receiving transducer. This system measures the elapsed time from when the sound pulse is transmitted to when the echo is detected to determine the exact range of the object from the transducers. The application shown in Figure 1(B) differs only in that a single transducer is used to transmit the sound pulse and receive the echo.

In some applications, such as high-speed counting and mechanical equipment positioning, it may be desirable to position the transducers opposing each other as shown in Figure 1(C). For clarity, the term "sensor" will be used in this article to describe either a single or dual transducer configuration.

Beam Angles and Side Lobes

Ultrasonic transducers are often designed to be directional so that the sound is efficiently transmitted or received only over a certain conical beam angle in front of the sensor. Ultrasonic transducers can be designed to produce any beam angle desired, from narrow (with beam widths of a just few degrees) to virtually omnidirectional. Some narrow beam transducer designs produce side lobes as the sound energy is transmitted; an example is shown in Figure 2(A). Advanced transducer designs eliminate all secondary side lobes and are more desirable for ultrasonic echo ranging; see Figure 2(B).

Different applications may require different beam angles for the sensors. In most cases, however, narrower beam angles are usually preferable to broader ones. A narrow beam angle system will not detect unwanted objects that are not in the insonified path of the transducer. (To insonify means to fill a specific volume with sound from a transducer.) Narrow beam angle systems are also less susceptible to background ultrasonic noise, and the systems will also operate over a greater range.

The beam angle of a transducer, alpha, is defined as the total angle between the points at which the sound power has been reduced to half its peak value. These are commonly referred to as the 3 dB down points. It is often advantageous to compute the spot diameter that is insonified by the ultrasonic beam. To calculate this spot diameter, use the formula:

D = 2 * R * tan(0.5 * alpha) where:D = spot diameter in inchesR = target range in inchesalpha = total beam angle in degrees

Frequency, Wavelength, and Attenuation

The operating frequency of a transducer, f, is predetermined by mechanical design. It should be selected after considering a number of factors such as transducer size, measurement resolution, background noise, and attenuation and range to the receiving transducer. The wavelength, lambda, of sound becomes shorter as the frequency increases. The relationship between frequency, wavelength and the speed of sound is expressed by: lambda = c/fwhere:lambda = wavelengthc = velocity of soundf = frequencySince the speed of sound changes with temperature, we must determine the current speed of sound before we can accurately calculate wavelength. At 0 C, the speed of sound is 13,044 in /s. At other temperatures use: CT = C0 sqrt(1+ (T/273)

where:CT = speed of sound at a specific temperatureC0 = speed of sound at 0 CT = temperature in degrees C

For example, using these two equations, the speed of sound at 25 C will be 13,628 inches/sec. At this temperature, the wavelength of sound at 215 kHz is 0.063 in. Because measurement resolution of ultrasonic systems is improved if the wavelength is shorter, applications requiring high resolution should use a transducer with the highest frequency possible in order to achieve the desired specification. As sound travels through air, its energy attenuates more rapidly if the frequency is increased. The maximum theoretical attenuation for ultrasonic sound (up to 200 kHz) may be calculated by this formula:

amax = f * 10-2

where:amax = maximum attenuation in dB/ft f = frequency in kHz

For example, using this equation, sound energy from a 215 kHz transducer would be attenuated a maximum of 2.15 dB/ft as it traveled through air. Attenuation may be less, depending on humidity, but is not so easily defined or calculated. Although attenuation limits the range of higher frequency transducers, there is a bonus: background noise at the same higher frequency is also Iess. Higher frequency ultrasonic sensors therefore, have a much better chance of working in an acoustically noisy environment than do lower frequency sensors. Beam angle also helps to lower background noise interference by limiting the transducer's noise sensitivity to the area defined by the beam angle of the sensor. Some transducer designs utilize a detachable horn. When the horn is attached, the beam angle of the transducer is reduced. This concentration of acoustical energy into a tighter beam increases the range of the sensor and reduces the background noise as well.

Environmental Factors

Temperature. The velocity of sound in air is 13,044 in./s at 0 C; it is directly proportional to air temperature (see above). As the ambient air temperature increases, the speed of sound also increases. Therefore if a fixed target produces an echo after a certain time delay, and if the temperature drops, the measured time for the echo to retum increases, even though the target has not moved. This happens because the speed of sound decreases, returning an echo more slowly than at the previous, warmer temperature. If varying ambient temperatures are expected in a specific application, compensation in the system for the change in sound speed is recommended.

Air Turbulence and Convection Currents. A particular temperature problem is posed by convection currents that contain many bands of varying temperature. If these bands pass between the sensor and the target, they will abruptly change the speed of sound while present. No type of temperature compensation (either temperature measurement or reference target) will provide complete high-resolution correction at all times under these circumstances. In some applications it may be desirable to install shielding around the sound beam to reduce or eliminate variations due to convection currents. Averaging the return times from a number of echoes will also help reduce the random effect of convection currents. Users addressing applications requiring high accuracy and resolution should evaluate these suggestions carefully.

Temperature variations and wind produce air turbulence that has various effects on the total performance of any ultrasonic sensing system, causing bending and distortion of the sound waves. The narrower the angle of the sound beam and the greater the distance to the target, the greater the turbulence. Additional signal processing may be able to filter data under high turbulence conditions to improve ranging information.

Atmospheric Pressure. Normal changes in atmospheric pressure will have little effect on measurement accuracy. Reliable operation will deteriorates however, in areas of unusually low air pressure, approaching a vacuum.

Humidity. Humidity does not significantly affect the operation of an ultrasonic measuring system. Changes in humidity do have a slight effect, however, on the absorption of sound. If the humidity produces condensation, sensors designed to operate when wet must be used.

Acoustic Interference. Special consideration must be given to environments that contain background noise in the ultrasonic frequency spectrum. For example, air forced through a nozzle, such as air jets used for cleaning machines, generates a whistling sound with harmonics in the ultrasonic range. When in close proximity to a sensor, whether directed at the sensor or not, ultrasonic noise at or around the sensor's frequency may affect system operation. Typically, the level of background noise is lower at higher frequencies, and narrower beam angles work best in areas with a high ultrasonic background noise level. Often a baffle around the noise source will eliminate the problem. Because each application differs, testing for interference is suggested.

Radio Frequency Interference. Another possible source of noise is RFI emitting from SCRs in a variable speed drive. Shielding around the back and sides of the transducer may prevent RFI noise from entering the system.

Splashing Liquids. Splashing liquids should be kept from striking the surface of the sensor, both to protect the sensor from damage if it is not splashproof and to ensure an open path for the sound energy to travel. Sensors used in a splashing environment, however, should be designed to operate when wet.

Mounting orientation is also a consideration in such an environment. Straight-down orientation can cause moisture to form as a large drop on the face of the sensor, reducing the efficiency of the system. Certain applications permit mounting the sensor so that it is aimed lower than horizontal but not pointed straight down; in this orientation, gravity will help to keep moisture from collecting on the face of the sensor.

Two methods may be used to improve the reliability of ultrasonics in the presence of splashing liquids. While beam bouncing (see Figure 3) provides a clever way of keeping the sensor out of the immediate area of splashing liquids, some applications don't lend themselves to this technique. An alternative method involves placing around the sensor a short tube that extends out past its face but not into the actual beam pattern. It is very important that the acoustic beam not be allowed to touch the edge of the tube; if it does, the tube might deteriorate the acoustic performance (see Figure 4).

Target Considerations

Composition. Nearly all targets reflect ultrasonic sound and therefore produce an echo that can be detected. Some textured materials produce a weaker echo, reducing the maximum effective sensing range. The reflectivity of an object is often a function of frequency. Lower frequencies can have reduced reflections from some porous targets, while higher frequencies reflect well from most target materials. Precise performance specifications can often be determined only through experimentation.

Shape. A target of virtually any shape can be detected ultrasonically if sufficient echo returns to the sensor. Targets that are smooth, flat, and perpendicular to the sensor's beam produce stronger echoes than irregularly shaped targets. A larger target relative to sound wavelength will produce a stronger echo than a smaller target until the target is larger than approximately 10 wavelengths across. Therefore, smaller targets are better detected with higher frequency sound. In some applications a specific target shape such as a sphere, cylinder, or internal cube corner can solve alignment problems between the sensor and the target.

Target Orientation to Sensor. To produce the strongest echoes, the sensor's beam should be pointed toward the target. If a smooth, flat target is inclined off perpendicular, some of the echo is deflected away from the sensor and the strength of the echo is reduced. Targets that are smaller than the spot diameter of the transducer beam can usually be inclined more than larger targets. Sensors with larger beam angles will generally produce stronger echoes from flat targets that are not perpendicular to the axis of the sound beam.

Sound waves striking a target with a coarse, irregular surface will diffuse and reflect in many directions. Some of the reflected energy may return to the sensor as a weak but measurable echo. As always, target suitability must be evaluated for each application.

Averaging. Certain applications involve a constantly moving target, such as the surface of agitated liquid in a tank. Analog outputs, which may be averaged by a Programmable Logic Controller or computer, will track the constant movement with little difficulty, but set point outputs might turn on and off unnecessarily as the target hovers around a set point distance. Hysteresis will prevent switched outputs from oscillating to a certain extent, but if the agitation or movement is great enough, the outputs will still switch on and off.

This problem can be easily solved in a number of ways. One method is to delay the decision process by using a time delay relay (TDR). A DC powered on-delay TDR may be directly connected to a set point output and programmed to delay switching on its output until it has received power for a specific length of time. The target will then have to be past the set point distance for that programmed time before the TDR will turn on, activating the primary load. Measurement can also be averaged with a Programmable Logic Controller (PLC) or an averaging digital panel meters. PLCs have done for industrial control what word processing has done for the modern officethey have provided flexibility and have reduced costs by greatly simplifying the wiring and troubleshooting of a complete process system.

Ultrasonic systems have also increased the flexibility of measurement and control systems used in typical applications. One ultrasonic system can often replace multiple photoelectric, capacitive, or mechanical limit switches and at the same time provide additional distance information. The fact that all measurements are made without physical contact with the target improves the lives of both the target and the sensing system.

Manipulating Liquids With Acoustic Radiation Pressure

At the NASA Lewis Research Center, high-intensity ultrasound is being used to create acoustic radiation pressure (ARP) on objects in liquids. It is also being used to create liquid currents or jets called acoustic streaming.

NASA's interest in ARP includes remote-control agitation of liquid systems in space, such as in liquid space experiments and liquid propellant tanks. It can be used to eject or deploy droplets for droplet physics or droplet combustion experiments. It can also be used to manipulate bubbles, drops, and surfaces suspended in liquid experiments and propellant systems.

Acoustic streaming.ARP agitation employs focus transducers to create agitating streams. The acoustic streaming can be used to suspend particles, mix liquids, and obliterate nonuniformities in temperature or concentration. Unlike conventional approaches, ARP agitation is nonintrusive, so there are no mechanical propellers, shafts, seals, or motors. Furthermore, it can be used to agitate sealed containers without external plumbing. Agitation can even be done without disturbing a liquid pool's surface.

ARP agitation with focused acoustic transducers.By introducing high-intensity sound waves into a syringe needle, one can use ARP to dispense a droplet on demand. This increases the reliability and repeatability for liquid-dispensing devices. The speed of the separation can be tightly controlled for space experiments. The device also can enhance the dispensing of coatings, adhesives, and solder pastes for the electronics industry.

ARP droplet deployment.The ultimate in flexibility is to use a high-power acoustic phased array to generate and direct ARP. The sound beam direction and focus is controlled electronically. An interactive, real-time system lets experimenters manipulate objects anywhere in a test volume. Because the acoustic phased array can emulate simpler acoustic devices, it can serve as a general purpose system fulfilling multiple roles. This approach can also be used to control the location of bubbles and voids in spacecraft propellant tanks. In addition, ARP has potential uses in medicine, such as in repositioning detached retinas.

ARP liquid manipulation by acoustic phased arrays.

Lewis contact: Richard C. Oeftering, (216) 433-2285, Richard.C.Oeftering@grc.nasa.gov Author: Richard C. Oeftering

Acoustic Radiation

An excellent route for learning about radiation in general, with applications to scattering and resonators.

Contents

i. Introductionii. Radiationiii. Scatteringiv. Resonatorsv. ReferencesIntroduction

This paper assumes prior knowledge of the properties of sound waves and the use of the vector potential. For an introduction to acoustics through plane waves, see Sound Waves . For an explanation of the wave equation, and the properties of its solutions, including amplitudes, interference and the use of phasors, see Wave Functions. For an exposition of the vector calculus, the velocity potential, and spherical wave solutions, refer to Waves in Three Dimensions . All this forms a comprehensive course in sound waves, but not in the vibration of material bodies, a subject usually closely associated with acoustics.

Radiation

The wave equation implies wave solutions: that is, disturbances that independently carry energy forward without a continuous motion of the medium supporting the waves. This is the very essence of wave motion, well shown by the plane wave solutions. But the wave energy must have had some source, and we must extract energy from the wave in order that it have some effect, so propagation by itself is not the whole story. When there is a localized source in a large volume, the energy moves outward along radial lines, at least at distances large compared to the size of the source, in the well-known rays, so this is phenomenon is called radiation.

Radiation involves not only the waves, but also their physical source and the interaction of the two, so its study is much more complicated than that of wave motion by itself. Electromagnetic radiation is one example of very great utility and interest, but it is rather complicated, not least because the vector nature of the waves must be explicitly treated. Also, it travels at the speed of light, which is a fundamental constant of relativity, making light a very special case of wave motion. Acoustic radiation is much simpler, because the waves may be described by a scalar, the velocity potential, they travel at lower and more comfortable speeds where relativity is not an issue, and their interpretation is concrete, the mechanical motion of a material medium. Many of the general properties of radiation will be common to light and sound, however, so that the study of acoustic radiation offers an understanding of electromagnetic radiation as well. A direct, plodding approach to radiation is impossibly difficult and unenlightening. It is necessary to apply intelligence and ingenuity to this problem, as in so many other endeavours, in addition to mathematical skill.

Our method of approach is as follows. We postulate that the wave equation is satisfied, so that we can make free use of superpositon. This allows us to make a Fourier transformation from time to frequency space or, what is the same thing, to assume a time variation eit. This agrees very nicely with the harmonic vibrations of solids that will be our sources. Then we look for solutions that represent outgoing (and perhaps incoming) waves, which seem appropriate to the geometry. If the constants in a solution can be adjusted so that the normal velocity is continuous at a bounday, then we assume that the result is the unique solution to our problem. If we had another solution that satisfied the same boundary conditions, then the difference of the two solutions would have a zero normal velocity on all boundaries, and would, therefore, be identically zero, showing that the two assumed solutions must actually be the same. This uniqueness proof deserves careful mathematical attention, which it has received. We simply use the results of these investigations in gratitude that the hard work has been done for us.

The simplest problem is a point source in infinite space, where we assume that all motion vanishes at infinity. The origin of coordinates is taken at the source. The simplest solution for this case is = C e-ikr/r, where C is a constant, k is the wavenumber, 2/, and r the distance from the source. The radial velocity is then v = C e-ikr/r2 + ik C e-ikr/r. The flux through a sphere of radius r is 4r2 v. As r is made very small compared to 1/k, the second term vanishes, while the first term gives 4C, a constant, showing that matter is created at the point at the rate 4C = q cm3/s. Of course, all these quantities are amplitudes multiplying the common time factor eit. We have found that the monopole source q gives rise to a velocity potential qe-ikr/4r.

It is instructive to note that the velocity consists of two terms with different radial dependences. When kr is small, the first term predominates, and is approximately q/4r2, precisely what you would expect if the medium were incompressible and the speed of sound infinite. The velocity is in phase with the source. When kr is large, the second term predominates. The velocity falls off only as 1/r, and is 90 advanced in phase. The first region is called the near field, differing little from potential flow in an incompressible medium, and the second the far field , where the 1/r dependence shows that energy in the wave is propagated to unlimited distance. The far field velocity results from differentiation of the retardation factor e-ikr. Radiation is, it may be concluded, a consequence of the finite speed of propagation of the wave.

The connection with incompressible flow is helpful in our study, since incompressible flow is easier to work with. In this case, the velocity potential satisfies Laplace's equation, which gives us many analogies with electrostatics and potential theory. To pass to the general case, we simply multiply by the retardation factor. Thus, = q/4r becomes = qe-ikr/4r. Note that we cannot apply retardation directly to the velocity, since the velocity does not satisfy the simple wave equation. By using frequency space and potentials, we easily glide by some very difficult mathematics with no loss of understanding.

The monopole source is not quite general enough for practical use. In electromagnetism, it does not exist at all, because of the conservation of charge. Two monopole sources of strengths +q and -q, separated by a distance a, form a new type of source when they are conceived as strengthening while approaching one another so that the product p = qa remains constant. This product is called the dipole moment, and its direction is considered as from the -q to the +q. Of course, dipoles are very familiar from electromagnetism. To find the potential of a dipole, we simply differentiate the monopole potential of a source q with respect to a distance x, obtaining = qxdx/4r3, and pass to the limit qdx = p. The result is most conveniently expressed as = p cos/4r2 , where is the angle between r and the direction of the dipole. The sign is easily determined by considering the velocity along = 0, which must be away from this positive end of the dipole. The potential in the general case is then (p cos)e-ikr/4r2.

The velocity for a dipole radiator can now be found by differentiation. There is a near field term with a radial component p(1 + ikr)e-ikrcos/4r3 and a transverse component half as large, varying as sin instead of cos . The far field term is purely radial, -k2p cos e-ikr /4r. Once p has been determined for the near field by applying the boundary conditions, it is also known for the far field. This is the connection between the boundary conditions and radiation.

Now we can solve a very interesting case. Consider a sphere of radius a, such that ka