Applied Acoustics 71 (2010) 793–800
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Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Near-ﬁeld characteristics of the parametric loudspeaker using ultrasonic transducers Hyeong Sick Ju a, Yang-Hann Kim b,* a b
Graduate Program in Acoustics, The Pennsylvania State University, 201 Applied Science Building, University Park, PA 16802, USA Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejon 305-701, Republic of Korea
a r t i c l e
i n f o
Article history: Received 27 June 2009 Received in revised form 16 November 2009 Accepted 13 April 2010 Available online 18 June 2010 Keywords: Parametric loudspeaker Near-ﬁeld Directivity Attenuation Spurious signal
a b s t r a c t A parametric speaker is a device for generating and focusing highly directional sound beams. It is essentially a by-product that comes with the nonlinearity of ultrasound. It is noteworthy that this directional beam was controlled and utilized mostly for far-ﬁeld applications in the past. We empirically study the directivity and attenuation characteristics of the parametric loudspeaker in the near-ﬁeld where we desire to use it. Physical parameters for experiments are imported from a theoretical model based on the far-ﬁeld approximation. The ﬁndings are that increases in aperture size and modulation frequency cause higher directivity, but have more than twice the beamwidth of the far-ﬁeld approximation. The attenuation also does not obey the inverse-square law which describes far-ﬁeld spreading from acoustic sources. The results conclusively explain a series of formation and attenuation of the virtual sound sources and deﬁne limitations of use in the near-ﬁeld. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction In recent years a new type of loudspeaker called the parametric loudspeaker has been developed to generate highly directional sound, and is now commercially available. Sound focusing by the parametric loudspeaker is utilized to deliver audible information to people in a particular region without disturbing others. The beam-like spreading of the focused sound can also be used for long distance communication and for generation of virtual sound on a wall by reﬂection. The parametric loudspeaker is based on parametric array theory, which has been utilized in underwater sonar for a few decades. The parametric array devised by Westervelt  consisted of multiple ultrasonic transducers and generated ﬁnite-amplitude ultrasonic carrier waves with two closely spaced frequencies. Nonlinear interaction of the two-tone waves produced a highly directional acoustic wave with a relatively low-frequency, which corresponded to the difference between the carrier frequencies. Amplitude modulation of the ultrasonic carrier waves introduced by Berktay  could substitute a frequency spectrum for the tonal difference-frequency. Since Bennett and Blackstock  successfully carried out the experiment of the parametric array in air, it has been utilized in audio applications by Yoneyama et al. . Serving * Corresponding author. Tel.: +82 42 350 3025; fax: +82 42 350 8220. E-mail addresses: [email protected]
(H.S. Ju), [email protected]
(Y.-H. Kim). 0003-682X/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.apacoust.2010.04.004
as a parametric loudspeaker, the audible sound beam could be generated by self-demodulation of the carrier ultrasound and by high directivity inherited from the parametric array. Various physical aspects of the parametric loudspeaker have been investigated as its applications increase. Kamakura et al.  introduced the rectangular aperture to the parametric loudspeaker, and Pompei  utilized the pre-processing scheme to reduce unwanted harmonic distortions. Karnapi et al.  enhanced low-frequency perception, and Kim and Sparrow  attempted the numerical analysis of the nonlinear sound generation. More recently, hardware design and fabrication were investigated by Roh and Moon , and a beamforming algorithm was developed by Yang et al. . These studies achieved notable improvement in signal processing and far-ﬁeld analysis and offer a few theoretical solutions. However, the spatial distribution of the audible sound beam has rarely been explored in the near-ﬁeld. It is important to investigate the practical near-ﬁeld characteristics of the audible sound beam because listeners are commonly placed in that region due to the limited installation space of the parametric loudspeaker. In this region, the ultrasonic carrier coexists with the generated audible sound and inﬂuences performance measurement. The inﬂuence of individual transducer units in the parametric loudspeaker may also not be ignored. For effective use under these conditions, it is necessary to directly measure and evaluate the directivity and attenuation of the parametric loudspeaker. These are meaningful because the directivity limits the focused region, and the attenuation determines the optimal
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Fig. 1. Schematic illustration of sound beam generation in the parametric loudspeaker. The shading of the virtual sources represents their decay with distance from the array.
distance for listeners. In this study, the directivity and attenuation characteristics are empirically studied by controlling relevant physical variables.
2. Theoretical background Generation of a low-frequency sound beam in the parametric array is explained by the nonlinear interaction of acoustic waves and the arrangement of virtual acoustic sources. As shown in Fig. 1, the parametric array usually employs multiple ultrasonic transducers which are regularly arranged on a source plane. Two groups of the transducers are excited with slightly different frequencies, whose difference corresponds to an audio frequency. Equivalently, all the transducers can be excited by a single carrier signal, whose amplitude is modulated by the audio signal. In both cases, the parametric array generates ﬁnite-amplitude acoustic waves which propagate as a collimated acoustic beam. These waves interact nonlinearly in the medium and produce an audible sound as a by-product, which forms virtual acoustic sources in space. As these virtual sources line up along the propagation path as a virtual end-ﬁred array, they provide high directivity. The ultrasonic carrier decays after propagating a sufﬁciently long distance, and only the audible sound survives and serves as a highly directional acoustic beam in the far-ﬁeld.The nonlinear interaction in 1-D space can be simply demonstrated by the computational analysis of the distortion of a tonal wave . As a ﬁnite-amplitude wave with frequency f0 propagates, its waveform changes into a sawtooth shape because phase velocities in the waveform vary with position; higher amplitude pressures propagate faster than lower amplitude pressures. The Fast Fourier Transform (FFT) of the waveform would show odd and even harmonics generation from the distortion. Similarly, when two-tone waves with frequencies fa and fb interact, the nonlinear distortion produces sum-frequency fa þ fb and difference-frequency jfa fb j components. As
Fig. 2. Coordinate system of the sound beam. The z-axis represents the beam axis along which the sound beam propagates.
the wave propagates a long distance, the two high-frequency (fa and fb ) and the sum-frequency (fa þ fb ) waves decay by absorption in air, whereas the difference-frequency wave (jfa fb j) survives. When an ultrasonic carrier is modulated, the audible sound is generated by the self-demodulation in a similar manner. In the 3-D case, the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation  describes the behavior of the sound beam, which is given by
@ 2 p c0 2 d @3p b @ 2 p2 r? p 3 3 ¼ @[email protected]
s 2 2c0 @ s 2q0 c30 @ s2
where p is the sound pressure, s ¼ t z=c0 the retarded time, c0 the sound speed, q0 the density, d the diffusivity for the thermo-viscous absorption, and b the nonlinearity coefﬁcient of the medium. In the coordinates shown in Fig. 2, the Laplacian r2? ¼ @ 2 [email protected]
2 þ r 1 ð@[email protected]
Þ is applied to the observer plane perpendicular to the beam axis, and the source size is deﬁned as a. The left-hand side of the equation describes the 3-D propagation of the sound beam: c20 r2? p de3 scribes diffraction related to the directivity, and 2cd3 @@ sp3 describes 0 the attenuation. The right-hand side of the equation is related to generation of the virtual sources by the nonlinear interaction. A closed-form solution of the KZK equation (1) is not known. However, its far-ﬁeld solution is available through a quasi-linear approximation which employs ﬁnite-amplitude and weak nonlinearity . This solution is written as
q ðr; zÞ ¼
DA ðhÞ ¼
2 jp0a p0b bk ea z jk tan2 h z ðhÞD ðhÞ exp D W A 2 z 4q0 c20 aT
2J 1 ðk a tan hÞ k a tan h
1 1 þ jðk =2aT Þ tan2 h
DW ðhÞ ¼
where p0 is the sound pressure amplitude of the ultrasonic carrier, k is the wave number, and aT ¼ aa þ ab a represents the total absorption coefﬁcient consisting of individual classical absorption coefﬁcients. The subscripts a, b, and minus () indicate the ﬁrst and second ultrasonic carriers and the difference-frequency wave, respectively. A few aspects of this solution are notable. The far-ﬁeld solution is the product of two theoretical directivities: the aperture factor and the Westervelt directivity. The aperture factor DA(h) accounts for a directivity pattern similar to that of a piston source in the far-ﬁeld, whereas the Westervelt directivity DW(h) accounts for the highly directional characteristic of the parametric array. Fig. 3a shows DA(h), DW(h), and their product. The conditions used to generate these were a 40 kHz carrier frequency, a 1 kHz modulating frequency and a 0.146 m source size. The comparison of these directivities indicates that both DA(h) and DW(h) may contrib-
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Fig. 3. Comparisons of directivities: (a) parametric loudspeaker, aperture factor and the Westervelt directivity and (b) parametric loudspeaker and piston source. Sound pressure level was normalized by the maximum on the beam axis and suppressed below 30 dB. Following assumptions were made: effective source size 0.146 m, audible frequency 1 kHz, carrier frequency of the parametric array 40 kHz, humidity: 30%, temperature: 20 °C.
ute to the directivity of the parametric loudspeaker, but DW(h) is dominant in the far-ﬁeld. This directivity is strongly inﬂuenced by sound absorption, which is determined by humidity and temperature in air. Ambient conditions (relative humidity: 30%; temperature: 20 °C) were assumed. Fig. 3b shows the directivity of the parametric loudspeaker compared with that of the conventional circular piston source with an equivalent source size and operating frequency. Apparently, the parametric loudspeaker in the far-ﬁeld shows a much narrow beam-pattern compared to the piston source as expected.The pressure amplitude of the difference-frequency wave is inversely proportional to the total absorption coefﬁcient and is attenuated as z1 ea z ; this complies with the inverse-square law when the absorption of difference-frequency a can be ignored. According to the inverse-square law, the sound intensity decreases by a factor of four and the sound amplitude by a factor of two as the observer distance z is doubled. For comparisons with the distance z, the virtual array length is deﬁned as lva = 1/aT and the Rayleigh distance as z0 ¼ pa2 =k, referenced to the far-ﬁeld. The ultrasound is regarded to decay considerably from absorption as it propagates after the array length. Far beyond the Rayleigh distance, acoustic waves spread out in obedience to the inverse-square law. It is notable that the approximate solution is applicable only in the far-ﬁeld region where strong absorption (z > lv a ) and spherical spreading (z > z0 ) are valid. So far we have reviewed the far-ﬁeld solution to predict the directivity and attenuation characteristics of the parametric loudspeaker. These factors are determined by the source size and the audio frequency in terms of the geometric and signal features of sound focusing devices. However, when the spatial criteria for lva and z0 are not satisﬁed due to the installation limitations as aforementioned, the sound focusing may be limited to the near-ﬁeld while requiring a proper controllability of the directivity and attenuation. In the near-ﬁeld these factors would be still subject to the physical parameters of the source size and the modulating audio frequency. Without known solution, the near-ﬁeld directivity and attenuation need to be empirically characterized by controlling these parameters and directly measuring the acoustic ﬁeld. For this purpose, a new type of the parametric loudspeaker prototype with ﬂexible source sizes and modulating audio frequencies is devised. Detailed procedures and considerations for the experiment are explained in the next chapter. The experimental result would be compared to the far-ﬁeld approximate solution to reveal the distinctive near-ﬁeld characteristics. 3. Experiments 3.1. Design of the parametric loudspeaker A prototype of the parametric loudspeaker was devised to control the selected physical variables. It consisted of a signal driving
unit and an emitter. In the signal driving unit, the modulated signal was generated by an arbitrary function generator and boosted by a power ampliﬁer. Multiple ultrasonic transducers (Sensortec ST203L), developed for distance measurement sensors, were utilized for the emitter. Each transducer was identically 1.8 cm in diameter and had a nominal capacitance of 2200 pF. According to the product speciﬁcations, the resonance and anti-resonance frequencies were 40.2 and 41.4 kHz, respectively, and the resonance impedance was 610 X. From these values, the mechanical Q-factor of the transducer unit was estimated to be about 52. The displacement amplitude of the transducer surface was measured by a Laser-Doppler-Vibrometer (Ometron VH300) when transducer was excited at its resonance frequency with voltages ranging from 30 to 150 Vp–p in 10 V increments. The results showed that the displacement linearly increase with increasing applied voltage within a 3% statistical error. The transducers were regularly arranged in a rectangular shape in an acrylic plate as shown in Fig. 4. These integrated transducers on the emitter formed the radiating surface of the parametric loudspeaker. The spacing interval between the transducers was chosen as 2 cm to maximize the radiated power of the transducer array . Individual transducers were connected to the signal driving unit through dip switches, which were utilized to adjust the effective source size of the emitter by turning them on and off. 3.2. Effective measurement method The audible sound from the parametric loudspeaker is generated by demodulation of the ﬁnite-amplitude ultrasound. However, when the ﬁnite-amplitude ultrasound is measured by microphones in the near-ﬁeld, the nonlinear distortion inside the microphones produces an additional unwanted signal. This is often called a spurious signal because it is not actually demodulated in air nor heard by ear . Even though the ultrasonic carrier undergoes strong absorption in air, it still coexists with the generated audible sound in the near-ﬁeld and inﬂuences the measurement of the audible sound level. Hence, more emphasis should be placed on the mechanism of the spurious signal generation from the measurement probe especially in the near-ﬁeld of the parametric loudspeaker. In a condenser-type microphone, acoustic pressure is sensed by the variation in electric charge, which is applied by constant external voltage and stored in an active capacitance between a diaphragm and a back-plate as illustrated in Fig. 5. The microphone diaphragm is made of a conductive membrane, which responds nonlinearly to the ﬁnite-amplitude acoustic pressure of the ultrasonic carrier, and results in inter-demodulation distortion of the electric signals. In addition, an electrical capacitance formed by clearance between the microphone housing and the back-plate contributes to the signal distortion, whose amplitude is approximately proportional to that of the measured ultrasound . Since the audible sound level of interest is often much less than that of
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Fig. 4. Prototype of the parametric loudspeaker: (a) dimension of components in the emitter and (b) picture of the prototype. Multiple ultrasonic transducers were embedded in a rectangular acrylic plate.
Fig. 5. Schematic diagram of spurious signal generation in the microphone. Ca: active capacitance between the diaphragm and the back-plate, Cp: parallel capacitance, and E0: external constant voltage.
the ultrasound, the spurious signal added to the audio signal changes the measured results considerably. Thus, it is necessary to minimize the spurious signal as much as possible. A dome-shaped acoustic ﬁlter was used as a physical low-pass ﬁlter to suppress the ultrasound and the spurious signal in the microphone , but this also decreased the audible sound level by 3 dB. To overcome this, an alternative technique was developed for this study. This technique utilized the sensitivity characteristics of the free-ﬁeld condenser microphone with varying incidence angles. Fig. 6 illustrates the response of a representative free-ﬁeld microphone whose sensitivity varies signiﬁcantly between the audible and the ultrasonic frequency regions. Because the sensitivity was ﬁrst corrected for microphone diffraction, the sensitivity decreases considerably as the ultrasonic waves excite the diaphragm at grazing incidence angles. The reduced sensitivity in high frequencies suppresses the amplitude of the measured ultrasound, while mostly preserving the sound level in the audio frequency range . As a result, this technique of tilting the microphone to a large grazing angle effectively prevents generation of the spurious signal. Simple measurements were carried out to verify this method. A free-ﬁeld microphone working within the audio frequency range was placed at 1 m from the acoustic sources (parametric loudspeaker and conventional loudspeaker) to be utilized in both normal and grazing incidence. In normal incidence, the microphone was placed in a position where its diaphragm was perpendicular to the wave propagation direction. Then its position was changed to be parallel to the propagation direction for grazing incidence. The audible sound from the conventional loudspeaker was mea-
Fig. 6. Illustration of the free-ﬁeld microphone response. The sensitivity of typical free-ﬁeld microphones may signiﬁcantly vary with incident angles in the ultrasonic region.
sured using the same free-ﬁeld microphone, and it was conﬁrmed that the incidence angle had a negligible inﬂuence on the measured audible sound pressure level. In the case of the parametric loudspeaker measurement, demodulated audible sound (1 kHz) was observed as shown in Fig. 7. The harmonics at 2 and 3 kHz, generally caused by the air-borne distortion from the parametric loudspeaker without pre-processing, were also observed. In contrast to the conventional loudspeaker, the variation of incidence angle decreased the level of the ultrasonic carrier (40 kHz) by 7.5 dB and the audio frequency (1 kHz) by 2.2 dB. Accordingly,
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the decreases in audible sound level corresponded only to the suppressed spurious signal. Based on this result, this method for suppressing the spurious signal was used in the directivity and attenuation measurements in this study.
3.3. Experimental setup
Fig. 7. Effect of the incidence angles (a) normal incidence (b) grazing incidence. The carrier frequency was primarily modulated by the audible sound of 1 kHz.
The directivity and attenuation were measured by an experimental setup as illustrated in Fig. 8. The emitter and measurement device were installed in an anechoic room to avoid any external noise inﬂuence. A two-channel function generator produced a 40 kHz ultrasonic signal along with a tonal audio signal. The ultrasonic signal was modulated by the audio signal in the generator and applied to the voltage-type power ampliﬁer. Passing through dual in-line package (DIP) switches, the ampliﬁed signal was sent to the emitter and converted into mechanical motion to generate the ultrasound. A free-ﬁeld microphone (B&K Type 4935), which generally serves as a component of microphone arrays and has a frequency limit of 5 kHz, was used for the measurement of the audible sound. To monitor the carrier ultrasound at 40 kHz, a broad-band microphone (B&K Type 4135) with a frequency limit of 100 kHz was utilized. The aforementioned method for suppressing the spurious signal can only be applied to the B&K Type 4935 microphone because its frequency range is far below the carrier frequency (40 kHz). The Rayleigh distance was calculated as z0 = 7.8 m, and the virtual array length as lva = 3.5 m. Sound pressures were measured within both distances. In these regions the quasi-linear solution of the KZK equation (2) would be invalid, therefore, the directivity and attenuation needed to be measured for comparisons.
Fig. 8. Schematic diagram of the experimental setup. Instruments: Tektronix AFG320 function generator, B&K Type 2173 power ampliﬁer, Agilent HP35670A FFT analyzer, B&K Type 4135 free-ﬁeld microphone.
Fig. 9. Schematic diagram of source size adjustment. a: effective source radius.
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Fig. 10. Directivity of various source sizes: (a) 0.146 m, (b) 0.135 m, (c) 0.129 m, and (d) 0.11 m. Sound pressure level was normalized by the maximum and suppressed below 30 dB.
Table 1 Beamwidth with varying effective source sizes. Number of transducers (rows columns)
Effective source radius (cm)
Beamwidth of the measurement (°)
(14 14) (14 12) (14 10) (14 8)
14.6 13.5 12.3 11.0
13.5 15.2 16.2 20.5
In the directivity measurements, the variations in sound level were recorded by rotating the parametric emitter on a turntable. From 90° to 90°, a total of 37 points were measured with 5° spacing. The beam axis of the parametric loudspeaker was located at 0° and aligned by beaming a laser from the center of the emitter to the microphone head. In the attenuation measurements, the microphone was transported away from the parametric loudspeaker surface. Sound pressure level was measured at 12 points
0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1.0, 1.2, 1.6, 2.0 and 2.4 m along the beam axis. These values were chosen with regard to distance doubling, e.g. 0.1–0.2 m and 0.8–1.6 m, to verify the inverse-square law. 4. Results and discussion 4.1. Near-ﬁeld directivity The directivity variation of the parametric loudspeaker was recorded by controlling the source size and the audio frequency of the parametric loudspeaker. As illustrated in Fig. 9, the source size was adjusted by turning-off the DIP switches from the edge and calculated as the radius of an equivalent-area circle. As shown in Fig. 10, directivity patterns of 5 kHz audible sound were measured at 1 m. Corresponding beamwidths were determined by the interpolation of the half-power angle where the sound level decreased by 3 dB from its peak. A third-order polynomial was used for the
Fig. 11. Directivity with varying audio frequencies measured at 1 m: (a) 500 Hz, (b) 1 kHz, (c) 2.5 kHz, and (d) 5 kHz. Sound pressure level was normalized by the maximum and suppressed below 30 dB.
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Table 2 Beamwidth with varying audible frequency. Audio frequency (kHz)
Quasi-liner solution (°)
0.5 1 2.5 5
55.6 39.1 26.9 13.5
26.0 18.3 11.2 7.44
interpolation near the peak of the measured directivity. Table 1 shows the increase in the beamwidth by reducing the source size; this was generally observed among linear acoustic sources. Fig. 11 shows the directivity patterns of the source with an effective size of 0.146 m at 1 m at four frequencies. The results were compared with the quasi-linear solution in the far-ﬁeld and the aperture factor under the same source conditions. Comparisons of the beamwidths as shown in Table 2 indicate that the directivity increases as the audio frequency increases. However, the measured results also show that the beamwidth is larger than the quasi-linear solution. This discrepancy implies the incomplete generation of the virtual sources in the near-ﬁeld. Within this region, the length of the virtual end-ﬁred array is insufﬁcient to produce the high directivity of the quasi-linear model. In addition, as the audio frequency increases, the measured beam-pattern approaches that of the aperture factor, which is similar to the far-ﬁeld beam-pattern of circular piston sources. Therefore, the measured results indicate that the directivity inherited from the equivalent linear piston source becomes dominant in the near-ﬁeld rather than from the Westervelt directivity. Accordingly, the use of the parametric loudspeaker as a highly directional beam source is considerably limited in the near-ﬁeld region. 4.2. Attenuation In the attenuation measurements shown in Fig. 12a, variations in the demodulated sound levels at 1 kHz and 5 kHz are plotted along with the ultrasonic carrier (40 kHz). The carrier has a much higher sound level and also decays faster than the demodulated tones. Fig. 12b and c compares the measured results with the approximate (quasi-linear) solution in the far-ﬁeld, which adheres to the inverse-square law. For both frequencies, the measured attenuation showed an irregular variation near the source plane. After that, the sound level decreases somewhat uniformly. The attenuation patterns show that the 1 kHz wave decays a little faster than the 5 kHz wave. This is because the attenuation is dominated by beam spreading instead of absorption at such low frequencies. The audible sound generated from the virtual sources also may attenuate as a spherically diverging wave after passing through the Rayleigh distance z0. Although the location where the divergence begins is not deﬁnite for the audible sound of the parametric loudspeaker due to the continuously distributed virtual acoustic sources along the beam axis, the Rayleigh distance of the low-frequency sound is generally much shorter than that of the high-frequency sound. This implies that the audible sound at 1 kHz diverges earlier than the sound at 5 kHz. Acoustic waves at both frequencies did not exactly follow the inverse-square-law. This is explained by the simultaneous formation and attenuation of the acoustic waves in the near-ﬁeld. The preexisting audible sound may decay as the distance increases, while the virtual sources generate a new audible sound in that region. This makes the prediction of the axial response of the parametric loudspeaker in the near-ﬁeld quite difﬁcult in contrast to the conventional acoustic ﬁeld where no virtual source exists. The parametric sound may eventually decay in accordance with the inverse-square law, as the observation distance is sufﬁciently
Fig. 12. Comparisons of attenuation (a) ultrasonic carrier and audible frequencies (b) 1 kHz and the quasi-linear solution (c) 5 kHz and the quasi-linear solution. The quasi-linear solution follows the inverse-square law in the far-ﬁeld approximation. Only the slope of the quasi-linear solution is valid for comparison because its reference point was arbitrarily selected near 0.5 m.
far from the parametric loudspeaker where the virtual acoustic sources no longer exists. The irregularity in attenuation is observed very near to the source plane, e.g. from 0.1 to 0.3 m; this implies that the formation of the virtual acoustic sources may not sufﬁce to generate the audible sound. Individual transducers have directional beam-patterns, which hinder the spatial coherence of the carrier ultrasound in that region. The inﬂuence of individual transducers may not be negligible because the audible sound directly generated by the nonlinear behavior of the transducer could be detected in spite of its low sound level. Practically, it is also difﬁcult to place the loudspeaker in such close proximity to listeners. 5. Conclusions In summary, the directivity and attenuation performance of the parametric loudspeaker was investigated by near-ﬁeld
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measurements. A theoretical model of the highly directional audible sound beam was revisited to import physical variables such as the effective source size and the audio frequency. These variables were utilized to control the experiments. Generation of an unwanted spurious signal in the microphone was effectively suppressed by a newly developed measurement technique. Findings in the directivity measurements indicated that the parametric loudspeaker had a highly directional pattern, but the decrease in difference-frequency and the effective radius widened the beamwidth of the audible sound. In the near-ﬁeld, the beamwidth was considerably wider than the predicted directivity from the quasi-linear solution. The measured attenuation in the near-ﬁeld did not comply with the inverse-square law, which was valid in the far-ﬁeld region. Therefore, these discrepancies imply the inﬂuence of the incomplete formation of the virtual sources and the simultaneous generation and attenuation of the audible sound in the near-ﬁeld. In this region, the use of the parametric loudspeaker may be limited to focusing on a small space, or to generate audible sound at relatively low-frequency ranges. The shortcomings in the near-ﬁeld applications may be somewhat overcome by simultaneously adjusting the source size with respect to the bandwidth. The relatively low attenuation in the near-ﬁeld can enhance the hearing of listeners, but unpredicted irregularity of the sound level is expected close to the parametric loudspeaker. This study also suggests that the inﬂuence of individual transducers should be investigated and controlled in the near-ﬁeld. Acknowledgements The authors wish to acknowledge valuable discussions with Dr. Seong-Woo Kang from Western Digital Corporation. We would also like to thank Dr. Sea-Moon Kim in Korea Ocean Research & Development and Dr. Sang-Ryul Kim from Korea Institute of Machinery & Materials for their considerable assistance with the power ampliﬁer. One of the authors (Hyeong Sick Ju) wishes to especially thank Douglas Dougherty with the Applied Research Laboratory at the Pennsylvania State University for his revision and technical advice. References  Westervelt PJ. Parametric acoustic array. J Acoust Soc Am 1963;35:535–7.  Berktay HO. Possible exploitation of nonlinear acoustics in underwater transmitting applications. J Sound Vib 1965;2:435–61.  Bennett M, Blackstock D. Parametric array in air. J Acoust Soc Am 1975;57:562–8.  Yoneyama M, Fujimoto J, Kawamo Y, Sasabe S. The audio spotlight: an application of nonlinear interaction of sound waves to a new type of loudspeaker design. J Acoust Soc Am 1983;73:1532–6.  Kamakura T, Tani M, Kumamoto Y, Breazeale MA. Parametric sound radiation from a rectangular aperture source. Acustica 1994;80:332–8.
 Pompei FJ. The use or airborne ultrasonics for generating audible sound beams. J Audio Eng Soc 1999;47:726–30.  Karnapi FA, Gan WS, Er M. Method to enhance low frequency perception from a parametric array loudspeaker. In: 112th Convention of the Audio Engineering Society, Munich, Germany, May 10–13, Paper 5636; 2002.  Kim W, Sparrow VW. Audio application of the parametric array – implementation through a numerical model. In: 113th Convention of Audio Engineering Society, LA, USA, October 5–8, Paper 5652; 2002.  Roh Y, Moon C. Design and fabrication of an ultrasonic speaker with thickness mode piezoceramic transducers. Sensor Actuat A 2002;99:321–6.  Yang J, Gan WS, Tan K-S, Er M-H. Acoustic beamforming of a parametric speaker comprising ultrasonic transducers. Sensor Actuat A 2005;99:91–9.  Novikov BK, Rudenko OV, Timoshenko VI. Nonlinear underwater acoustics. New York: American Institute of Physics; 1987. p. 21–3.  Hamilton M. Sound beams. In: Hamilton M, Blackstock D, editors. Nonlinear acoustics. New York: Academic Press; 1998. p. 233–52.  Lee H, Tak J, Moon W. Effects of mutual impedance on the radiation characteristics of transducers array. J Acoust Soc Am 2004;115:666–79.  Frederiksen E. Reduction of nonlinear distortion in condenser microphones by using negative load capacitance. In: Proceedings of Internoise 96, Liverpool, UK; 1996. p. 2679–84.  Kinsler LE, Frey AR, Coppens AB, Sanders JV. Fundamentals of acoustics. 4th ed. New York: John Wiley & Sons; 2000. p.420.
Hyeong Sick Ju was born in Cheonan, the Republic of Korea in 1978. He earned his B.A. degree in Mechanical Engineering from Yonsei University, Seoul in 2004 and M.S. degree from Korea Advanced Institute of Science and Technology (KAIST), Daejeon in 2006. Currently, he is a Ph.D. candidate in the Graduate Program in Acoustics and is also working as a research assistant in Engineering Nanostructure Characterization Center at the Pennsylvania State University. His research interests include physical acoustics, ultrasonic transducers, surface acoustic wave propagation, and acoustic microscopy.
Yang-Hann Kim earned his Ph.D. degree in the ﬁeld of acoustics and vibration at M.I.T. in 1985. He had worked for ﬁve years in the Department of Mechatronics at the Korea Institute of Technology as an Assistant and Associate Professor. He is currently a professor in the Department of Mechanical Engineering at Korea Advanced Institute of Science and Technology. He is a member of Sigma Xi, KSME, ASME, ASA, INCE, the Acoustical Society of Korea, and the Korea Society for Noise and Vibration (KSNVE). He was a director and chairman of the Research and Education Division of Acoustical Society of Korea from 1989 to 2000. He also served KSNVE as the editor of the KSNVE journal from 1992 to 1996, and has been on the editorial board of Mechanical Systems and Signal Processing (MSSP) and the Journal of Sound and Vibration (JSV). His main research interests include sound ﬁeld visualization, noise source identiﬁcation using array microphones, detection and estimation of moving noise source, generation of acoustically bright and dark zone, structural acoustics, duct acoustics, silencer design, diagnostics of machines and active noise/vibration control.