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Three-Dimensional Sound Intensity Measurements Using Microflown

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Three-Dimensional Sound Intensity Measurements Using Microflown THREE-DIMENSIONALSOUND INTENSITY MEASUREMENTS USING MICROFLO WN PARTICLE VELOCITY SENSORS Hans-Elias de Bree*, W.F. Druyvesteyn"", E. Berenschot*, M. Elwenspoek" * Micromechanical Transducers Group **LaboratorySignals & System Network theory University of Twente, P.O. Box 217,7500 AE Enschede, The Netherlands ABSTRACT This paper reports on a novel method to measure three-dimensional sound intensity and the fabrication of a miniature three-dimensional sound intensity probe. Verifying measurements where performed with three separate micro-machined particle velocity probes and one pressure microphone. A three-dimensional sound intensity probe has been realised based on a three- dimensional micro-machined particle velocity microphone, a 3D Microflown, and a miniature pressure microphone. INTRODUCTION A few years ago I had a discussion with the measurements. It consists of two very closely sales representative of a leading sound & spaced (40pm apart) heated platinum resistive vibration company. He claimed that the one temperature sensors. The temperature that was able to make a broadband sound difference of both sensors is linearly dependent intensity probe smaller than a sugar cube on the particle velocity. In combination with a should become a .wealthy person. Well, still pressure microphone a Microflown can form a poor but proud we present the miniature three- sound intensity probe, a so called p-U method, dimensional sound intensity probe. see Fig. 2 [3]. Sound intensity is a vector quantity, defined A one dimensional sound intensity probe as the time averaged product of the sound can be extended to a three dimensional probe pressure (a scalar quantity, p) and the by using three p-p probes (six microphones) or corresponding particle velocity (a vector one microphone and three Microflowns (p-u3). quantity, U) at the same position. The The realisation of a three-dimensional p-p measurement permits the determination of probe however is not very realistic. The prize radiated sound power without requiring special of such probe will be over 30,000 USD and the acoustic environments such as reverberation frequency range is limited even more than the and anechoic chambers. The measurement 1D p-p probe. technique is alsa used for sound source A broad band three-dimensional sound localisation. intensity probe however will offer many Since historically no particle velocity probes advantages. The magnitude and direction of the were available, the traditional way to measure acoustic energy flow can be measured directly, sound intensity was to use two closely spaced this will improve the effectiveness of the and phase matched pressure microphones. The measurement. The 3D measurement allows particle velocity is calculated by the difference measuring non-stationary sound fields as for of the signals from both the pressure example the noise of moving objects like microphones and the (average) sound pressure aeroplanes. is found from the sum of both. This method is Using of Microflown technology, a three- called the p-p method, see Fig. 1 [l]. dimensional sound intensity probe become Two major disadvantages of the p-p probe feasible. are its high prize and the fact that performing Preliminary measurements with three broad band measurements is time-consuming. separate (half-inch packaged) Microflowns and Furthermore the bandwidth of the probe is a half-inch pressure probe showed promising limited and the probe is fragile. results. Nowadays the Microflown [2] can perform Now a fully integrated three-dimensional the particle velocity measurement directly and Microflown has been realised. This will be a sound intensity measurement becomes another step in the direction of realisation of a possible without the mentioned disadvantages. rugged broad band three-dimensional sound A Microflown can be considered as a mass intensity probe. flow sensor that has been optimised for sound 0-7803-5194-0/99/$10.00 01999 IEEE 124 SOUND INTENSITY By measuring the pressure at two points at a close distance dr, the pressure gradient is Sound intensity is a vector quantity that approximated. describes the amount and direction of net flow of acoustic energy at a given position. It is defined as the time averaged product of the sound pressure (a scalar quantity, p) and the corresponding particle velocity (a vector This approximation is valid as long as the quantity, at the same position. separation, dr, is small compared to the U) wavelength. 1 I = - Ip(t)* u(t)dt BANDWIDTH(P-P) T The proper determination of the particle The electrical analogy is well known: velocity is frequency limited. The upper power=voltage x current. frequency is limited due to the fact that the Two methods to measure: the sound intensity estimation (dp/d-=(pa-pb)/dr)no longer holds. will be explained briefly: the p-p probe and the The lower frequency limit is caused by the p-U probe. For simplicity first the two methods phase mismatch of the two microphones and will be compared in their one directional electronics. realisation. The pros and cons will be extended In practice this means that the lowest later to the three dimensional versions. frequency that can be measured is best case (anechoic conditions) 20Hz and worst case THEP-P PIROBE 3 50Hz (reverberation, phase mismatch=0.3"). The smallest size of the microphone separation A p-p probe consists of two, closely spaced, equals the microphone diameter and bounds the matched pressure microphones [ 11. highest frequency that can be measured (approximately 1OkHz). SPACERS(P-P) To measure the complete bandwidth with a p-p probe three spacers and two types of microphones are used. Two half inch microphones and a spacer of 50" are used for the lower frequencies (20-350Hz to 1250Hz) the 12" spacer is used for the medium frequencies (250-1250 to 5kHz). Two Fig. 1: ID p-p B&K sound intensity probe (The quarter inch microphones and a spacer of 6mm microphones are a half inch in diameter). are used to measure in the higher frequencies The particle velocity is calculated by the (250-2000 to 1OkHz). The p-p probe has to be subtraction of the signals from both pressure disassembled and re-calibrated when changing microphones, The method is based upon spacers or microphones. This makes the broad Newton's second law, the equation of motion: band sound intensity measurement time consuming furthermore the use of these spacers will make the realisation of the probe fragile. NEARFIELDMEASUREMENTS (P-P) Where p is the density of the medium, ur is When a p-p probe is positioned in the the particle velocity in one direction r, and p nearfield of a sound source, the sound intensity the instantaneous pressure. Since the pressure is not constant from one pressure probe to the gradient is proportional to the particle other. This will lead to an overestimation. This acceleration, the particle velocity can be effect is present when the probe is placed obtained by integrating the pressure gradient in closer to the source than at least two times the respect to time. separation (of the microphones) and can be a problem at low frequencies. U, =-- I+j-dt Pa 125 THEP-U PROBE SIGNAL TO NOISE RATIO (P-P) Historically there has been a lack of particle An example of a high quality matched pair velocity probes. Nowadays the Microflown [2] is the Briiel & KjEr sound intensity can perform the particle velocity measurement microphone pair B&K 4181 [5]. One of the % directly and a p-U probe can be realised [3]. inch matched microphones has a selfnoise of The probe consists of a pressure microphone 20dB(A) and a sensitivity of 11.2 mV/Pa (at and a particle velocity microphone. 1kHz) . It will be convenient to express noise values in voltages and in one Hertz bandwidth. The noise is expressed in VIdHz. The latter corresponds to: U,,,,, =3 1.6nV/dHz at 1 kHz [51. ( Usrgna[=l1.2mV at 1 Pa (=94dB SPL) pressure at 1 kHz). The microphones do have a l/f noise behaviour that will be dominant at frequencies Fig. 3: ID p-U sound intensity probe (The under 500Hz [SI. Because the differential microphone and Microjlown are a half inch pressure is measured to determine the particle in diameter). velocity, two microphones are used, the total The Microflown has a first order frequency noise will increase by a factor 42. This is behaviour. For low frequencies (f<300Hz) the depicted in Fig. 2. A plane wave with a sound frequency response will be flat and the phase intensity level of 94dB is offered to the p-p shift will be zero degrees. For higher probe. The signal (that will be used to calculate frequencies the (P3kHz) the frequency the particle velocity) is produced by the response will be exactly -6dB/oct and the phase subtraction of both pressure microphone shift will be -90 degrees. At its corner outputs. frequency the Microflown has a -3dB response Output voltages of a P-P probe and a phase shift of -45 degrees. It is not very difficult to correct the frequency behaviour of the Microflown electronically. BANDWIDTH(P-U) IOOpV - The bandwidth of a Microflown and a Non reactive field pressure microphone can not be compared Strona reactive field easily. Above the corner frequency a pressure 10pV - microphone can not be used. The Microflown 74dB however has an exact first order frequency 1 1- I behaviour. Therefore the Microflown can be used above its corner frequency. The present 100nV value of the corner frequency is 1kHz. 31.6nV For sound intensity purposes the lowest usable frequency will be determined by the pressure microphone and can be found lower Fig. 2: Noise output voltages in V/&z and ,i&uls due to 94dB SIL than IHz. It is hard to give a distinct high frequency As can be seen in Fig 2, when the frequency limit of a p-U probe.
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