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Producing an intense collimated beam of sound via a nonlinear ultrasonic array
Article in Journal of Applied Physics · June 2012
DOI: 10.1063/1.4729265
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Producing an intense collimated beam of sound via a nonlinear ultrasonic
array
Daniel Gibson, Martin Smith, John Scales, and Brian Zadler
Citation: J. Appl. Phys. 111, 124910 (2012); doi: 10.1063/1.4729265
View online: http://dx.doi.org/10.1063/1.4729265
View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v111/i12
Published by the American Institute of Physics.
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JOURNAL OF APPLIED PHYSICS 111, 124910 (2012)
Producing an intense collimated beam of sound via a nonlinear
ultrasonic array
Daniel Gibson,1,2 Martin Smith,3 John Scales,1 and Brian Zadler4
1
Department of Physics, Colorado School of Mines, Golden, Colorado 80401-1887, USA
Systems Biology, Harvard Medical School, 200 Longwood Ave, Warren Alpert 536, Boston,
Massachusetts 02115, USA
3
Blindgoat Geophysics, 2022 Quimby Mtn. Rd., Sharon, Vermont 05065, USA
4
Applied Research Associates, Inc., 7921 Shaffer Parkway, Littleton, Colorado 80127, USA
2
(Received 16 November 2011; accepted 14 May 2012; published online 26 June 2012)
We have designed and built an ultrasonic parametric array with an emphasis on creating an
intense, collimated beam of low frequency sound. With this device, we can insonify a small area
of ground or a small target at range and induce vibrations. These vibrations can be synchronously
detected with any stand-off device such as a laser-Doppler vibrometer or the millimeter wave
vibrometer we describe in Smith et al. [J. Appl. Physics 108, 024902 (2010)]. Despite nonlinear
conversion losses, the array produces sound pressure levels in excess of 90 dB at 1 kHz, 1.5 m in
C 2012 American Institute of Physics.
front of the array using 25 low-cost 40 KHz transducers. V
[http://dx.doi.org/10.1063/1.4729265]
INTRODUCTION
The goal of this work is to produce an intense, collimated beam of low-frequency (200 Hz 1000 Hz) sound
that can be used to insonify (i.e., couple sound into) as small
a target area as possible. One approach to producing such a
beam is to use a linear array of low-frequency sources in an
end-fire configuration. The angular width, d, of a monochromatic beam is approximately2
k
d¼ ;
L
(1)
where k is wavelength and L is the length of the array.
Assuming a speed of sound around 343 m=s, a 5 beamwidth we would need an array about 11k long. At 1000 Hz, a
5 array would be 3.8 m long, while at 500 Hz, it would be
7.5 m long.
A linear array larger than 3 m would be cumbersome,
space-consuming, and difficult to manipulate. A lighter,
more compact system would allow the array to be mounted
on the front of a vehicle where it may, for example, be used
in land mine detection. Such a system could exploit parametric array technology3–5 which allows the replacement of a
physical array by a virtual array created by nonlinear downconversion of intense sonic beams. Stepping through an
example, Figure 1 diagrams the process approximately as it
occurs in the specific parametric array used in this project.
The array emits two co-propagating beams whose difference frequency is the desired low-frequency. When the signals are of high enough amplitude, their propagation in the
interaction zone is non-linear. This is described by the
Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, which
takes into account nonlinearity, absorption, and diffraction.6
In first-order nonlinearity, the output signals consist of the
two input signals, their sum and difference, and harmonics
0021-8979/2012/111(12)/124910/4/$30.00
of the two input signals. The output frequencies include
x1 ; x2 ; ðx1 x2 Þ; ðx1 þ x2 Þ; 2x1 ; 2x2 , etc.
The distribution of output energy over the various frequency components is sensitive to the drive level, with
higher harmonics growing in amplitude as drive increases. In
our tests, we used a source waveform constructed from two
sinusoidal terms. The drive level was kept below the level at
which higher harmonics (see Figure 7 below) predominate
and the drive duration was kept short enough to avoid excessive transducer heating, typically a few seconds of signal. (In
Ref. 1, we show that our millimeter wave interferometer can
achieve 1 lm resolution given 1 s of signal.)
In our work, the drive frequencies were 40.5 kHz and
41.5 kHz leading to an acoustic difference frequency of
1 kHz. The low-frequency energy is generated throughout
the interaction volume and has precisely the phase distribution needed to function as an end-fire array along the axis of
the interaction zone. This results in the ability to use a physically compact source element, the ceramic transducer array,
to generate a collimated, low-frequency sonic beam that
would otherwise require a much larger source element. The
principal downside of the parametric array process is the typically low nonlinear conversion efficiency.6
In order to achieve as large an interaction zone as possible, the transducers must be driven as efficiently as possible
at high power levels. We used an array of 25 medium-power
(Airmar AR41) air-coupled transducers, each driven by a
separate 60 W amplifier (Marchand PM221) through a handwound matching transformer tuned for each transducer
(Amidon Ferrite Pot Core PC-1107-77). Figure 2 shows photos of the system during indoor testing.
The amplifier bank is mounted below the transducer
array along with the power control unit. The transducer=
transformer units are connected to the amplifiers via a patch
panel, making it easy to replace transducers. Transformers
111, 124910-1
C 2012 American Institute of Physics
V
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124910-2
Gibson et al.
FIG. 1. In this system, each ultrasonic transducer is a cylindrical element
92 mm in diameter which produces an ultrasonic beam in the vicinity of its
broad resonance. The nominal beam width of one transducer at 40 kHz is
14 . The transducer is driven with the sum of 40.5 kHz and 41.5 kHz sinusoidal signals. The transducer produces two ultrasonic beams, one at each frequency, of similar spatial characteristics. The zone where both beams have
high intensity is shown as an elongated oval.
mounted on the back of the transducers are used to obtain
maximum power transfer from the amplifier to the transducer
by matching the real component of the transducer’s electrical
impedance (from 40:5 kHz to 41:5 kHz) to the amplifier’s
ideal load of 4 X. The transducer behaves inductively at
those frequencies, so capacitance is added to the circuit to
minimize complex impedance in the amplifier’s load.
TESTING
First, in the lab, the amplitude of the difference frequency of 1 kHz was measured in a plane in front of the
parametric array using an audio microphone. The input voltage to the amplifiers was kept constant at 1 V peak to peak.
J. Appl. Phys. 111, 124910 (2012)
FIG. 3. A thermal image of the parametric array in operation. The difference in temperature between the working transducers is likely attributable to
imperfections in electrical impedance matching between the amplifiers and
the transducers, as well as small differences in the transducers themselves.
At this input voltage, the amplifiers draw approximately 5 A
total. A thermal infrared image of the system in action is
shown in Figure 3.
The interaction zone of the ultrasonic frequencies can be
characterized by the amplitude of the 1 kHz waveform along
the axis of propagation. This was sampled in variable increments of distance in front of the array, ranging from 1 cm,
where the slope of the amplitude is relatively high, to
150 cm, where the amplitude changes little with distance.
The result is shown in Figure 4.
The beam spreading is characterized by the angle of a
6 dB (full width at quarter maximum (FWQM)) contour in
the direction transverse to propagation.
FWQM ¼ ðPeak Amplitude 6 dBÞ:
FIG. 2. Parametric array and millimeter wave interferometer on mobile,
battery-powered cart.
(2)
FIG. 4. Amplitude of 1 kHz waveform as a function of position relative to
the center of the parametric array. The peak amplitude is reached around
100 cm, were it stays relatively constant. Using a sound pressure level meter,
we measured the 1 kHz sound pressure level (SPL) at 150 cm to be over
90 dB. In this plot, the measurements were made with a flat response microphone but with no absolute power capability. Thus, the vertical scale is relative to an arbitrary but fixed reference voltage.
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124910-3
Gibson et al.
J. Appl. Phys. 111, 124910 (2012)
FIG. 7. Far-field beam divergence measured outdoors at 10 m distance from
the array. The resulting beam divergence is consistent with the near field
measurements made in the laboratory.
FIG. 5. Beam intensity in a horizontal plane in front of the array. The average beam width, 18 , is shown by blue lines.
The data for a given distance in the direction of propagation
(Figure 5) are interpolated via cubic splines, then solved for
the FWQM. These are divided by two to give the average
distance off-axis, and fit using a linear, least squares regression to give beam width as a function of axial distance. The
slope of this result, m, is used to calculate the beam
spreading
havg ¼ 2 arctanðmÞ;
which is shown as lines in a contour plot of the beam intensity as a function of distance. The beam spreading is approximately 18 (i.e., beam divergence approximately 9 ). Even
though this result is measured in the near field, it is consistent with a coarse scan made at 10 m in field tests. This angle
is larger than we had hoped for but still gives an array size
roughly half that associated with a linear transducer array.
Repeated measurements of the same spatial location varied within 1 dB, which is taken to be the precision of the
measurement. The measurements far off-axis varied on a
shorter timescale (that of the oscilloscope averaging time) as
a result of low signal to noise ratio at low amplitude.
We looked at the presence of higher order term in the
response as the drive voltage increased (i.e., term associated
with cubic, quartic, etc., nonlinearities). As can be seen in
Fig. 6, the beat frequency is overtaken as higher harmonics
begin to dominate the signal. These can be heard as distortion of the beat note. The transducers themselves can withstand much higher driver levels provided the duty cycle is
short enough. Thus, in short burst mode, higher harmonics
could be exploited to produce a variety of beat frequencies
(the acoustic analog of 3-photon and higher processes.)
Finally, we performed a coarse beam divergence measurement at 10 m distance (Figure 7). This far field measurement
is in reasonable agreement with the beam width inferred
from the detailed amplitude map shown in Figure 5 measured in the laboratory.
CONCLUSION
We have constructed an ultrasonic parametric array
which provides a collimated beam of low-frequency sound
from a compact device. Results demonstrate a nonlinear
interaction zone of approximately 1 m within which the lowfrequency beat note is produced from the modulated ultrasonic signal, which is the sum of two nearby sinusoidal
signals. Apart from the matching transformers, the system
was built with off the shelf components and can be readily
expanded to increase the total acoustic power. Field tests
show that the array is still easily audible at over 100 m distance, while at 1:5 m the measured sound pressure level is
over 90 dB.
ACKNOWLEDGMENTS
FIG. 6. Beat tone (i.e., second harmonic) generation is overtaken by higher
harmonics which grow as powers greater than 2 of the driving amplitude.
This is a field test of harmonic line strength at 10 m distance from the array.
This work was partially supported under two grants
from the Army Research Office (W911NF-07-1-0478 and
W911NF-09-1-0533) and the U.S. Office of Naval Research
as a Multi-disciplinary University Research Initiative on
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124910-4
Gibson et al.
Sound and Electromagnetic Interacting Waves under Grant
No. N00014-10-1-0958.
1
M. L. Smith, J. A. Scales, M. Weiss, and B. Zadler, J. Appl. Phys. 108,
024902 (2010).
2
J. E. Barger, in Handbook of Acoustics, edited by M. J. Crocker (Wiley,
Hoboken, NJ, 1998).
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J. Appl. Phys. 111, 124910 (2012)
3
P. Westervelt, J. Acoust. Soc. Am. 35, 535 (1963).
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5
F. J. Pompei, “The audio spotlight: Put sound wherever you want it,”
J. Audio Eng. Soc. 47, 726–731 (1999).
6
R. T. Beyer, Nonlinear Acoustics (Naval Sea Systems Command, U.S.,
1974).
4
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