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A technique for the dynamic calibration of microphones and pressure transducers at high sound pressure levels
Journal of Sound and Vibration (1974) 32(4), 443--447
A TECHNIQUE FOR THE DYNAMIC CALIBRATION OF MICROPHONES AND PRESSURE TRANSDUCERS AT HIGH SOUND PRESSURE LEVELS D. JONES Hawker Siddeley Dynamics, Hatfield, England AND
T. V. JONES
Department of Engh~eerhlg Science, University of Oxford, Oxford OX1 3PJ, England
(Received 28 August 1973) A technique is described which enables microphones and pressure transducers to be dynamically tested at the sound pressure levels currently experienced in some vehicle and industrial environments. This employs a piston which is moved impulsively in a tube and generates a pressure pulse of calculable magnitude. Experimental results are presented which confirm that pressure pulses of the magnitude expected by theory are produced. I. INTRODUCTION High sound pressures of order 1 Ibf/in2t r.m.s. (~171 dB SPL) are of concern in some vehicle and industrial environments. The environments may be transient, as in the case of sonic booms, or sustained, as in the case of noise associated with powerful motors. To ensure accurate measurement of such fields methods of calibration of pressure transducers at high dynamic pressures are necessary. The calibration techniques currently in use have been summarized in references [1] and [2], where it can be seen that the shock tube is a primary technique commonly used at high pressures. However, in the case of microphones, calibration at atmospheric pressure is often necessary and hence a very weak shock wave is required. The pressure rise across a weak shock wave depends on the difference between the shock velocity and that of sound and as the measured quantity is the shock wave velocity the errors in determining the pressure rise may be large [2]. In the apparatus described here a pressure pulse similar to that in a shock tube was produced; however, it was generated by moving a piston impulsively in a tube and not by bursting a diaphragm. The magnitude of the pressure pulse was linearly related to the piston velocity in the acoustic approximation and this velocity was measured. In the following a description of the apparatus and the results obtained are given. The experiment was conducted in order to test the feasibility of the device and the resulting pressure pulses were measured by using a commercially available piezo-electric pressure transducer mounted in the reflecting end wall of the tube. The results obtained demonstrated that the method provides a simple means of dynamic calibration at high sound pressure levels. t l lbf/in2 ~ 6.9 kN/m2. 443
444
D. JONESAND T. V. JONES 2. THEORY
In a weak pressure wave the increase, p, above the ambient pressure, P, may be related to the flow velocity, v, by +
+ ...,
(])
where c is the ambient velocity of sound. On reflection from a rigid wall the pressure at the wall, Pa, is given by +....
(2)
In the acoustic limit v ~ c and equation (2) becomes PR -
P -
2Vv =
(3)
c
For the case considered here of a piston in a tube, where the piston accelerates over a short period and then decelerates slowly and is finally brought to a sudden halt, the variation of pressure at the reflecting wall is shown in Figure 1. This may be described in general by the equation (4) /'I=0
ILIIL"
(o) 0
b
C
(b)
(c)
p. I
!
t
|
I
Figure I. (a) Schematic diagram of the experiment: a, piston; b, compression wave; c, pressure transducer. (b) Ideal piston velocity history, v v e r s u s t . (c) Pressure at the reflecting wall; - - . , multiple reflections; , single pulse due to limited piston motion.
DYNAMICCALIBRATIONAT HIGH SPL
445
where v(t) is the pistol velocity at time t and H(y) is the Heavyside function obeying H = 0 for y < 0 and H = 1 for y > 0. I is the distance between the piston and the reflecting wall, which is assumed to be constant. In the experiments to be described the piston was brought to rest soon after acceleration and hence the rarefaction resulting from this reached the reflecting wall before any reflections from the piston, giving the pressure as shown by the dotted line in Figure 1. This enabled the time during which the piston was moving to be found from the pressure at the reflecting wall, and hence the average piston velocity, as the piston movement was known.
3. APPARATUS The apparatus is shown in Figure 2. The 2.54 cm diameter tube was 60 cm long and mounted vertically, the piston being at its lower end. The latter was made of brass and was covered with a P.T.F.E. sleeve so as to be a close fit in the tube. The top of the tube was blanked off by a flange in which was mounted a Kistler 701S piezo-electric pressure transducer whose output was displayed on an oscilloscope. The piston motion was produced by allowing a secondary piston to strike a rod attached to the bottom of the piston although
Figure 2. A diagram of the apparatus: a, Kistler 701S; b, copper tube; c, rubber section; d, P.T.F.E. sleeve; e, piston; f, P.T.F.E. guide; g, spacer; h, P.T.F.E. block; i, solenoid; j, secondary piston; k, stop.
446
D. JONES AND T. V. JONES
the motion was limited to a few millimeters. The secondary piston movement was produced electromechanically by using a solenoid through which a capacitor bank was discharged. In this manner the piston motion was impulsive and velocities up to 5 ms -1 were achieved. Half-way along the tube was a short section of nitrile rubber which served the purpose of reducing the effect of mechanical vibrations travelling up the tube and producing spurious transducer signals. 4. R E S U L T S
Typical transducer output signals may be seen in Plate 1. In Plate l(a) is shown the "staircase" in pressure due to multiple reflections when the piston motion was not limited, whereas Plate l(b) shows the single pulse resulting when only a small piston movement was allowed. The single pulse results were those analysed in the experiment. From traces such as that shown in Plate l(b) the time during which the piston was in motion could be measured and as the piston movement was limited to a known distance the average piston velocity, ~, could be found. The average pressure within the pulse,/~R, was measured, the manufacturer's calibration checked at high pressure with a shock tube being used, and this is plotted against iri Figure 3 for two values of piston movement. As/~R is linearly related to o by the acoustic approximation (equation (3)) the following equation should hold" PR --
P
2~,~ =
(5)
c
This is plotted in Figure 3 where good agreement with the experimental results is shown. A measure of the rise time of the pressure pulse achieved in the experiments is shown in Figure 4, where the time to reach half of the plateau value is plotted v e r s u s the average piston velocity. As may be seen, rise times of order 100/ts are approached at high velocities.
I
I
I
I
/
x,r 4 9
I
.4-
-4-
+
3
2 o
I
0
Lf
I I
I 2
I $
I 4
I 5
~" ( m / s )
Figure 3. The average pressure rise at the reflecting wall,/~, v e r s u s the average piston velocity, t~, and a comparison with theory (equation (5)). Piston movement: o, 2.02 mm; +, 3-84 mm; , acoustic theory (equation (5)).
Plate 1. Typical reflected pressure outputs. (a) Multiple reflections; sensitivity, 4 x 10 -2 atm/cm; timebase, 5 ms/cm. (b) Single pulse; sensitivity, 10 -2 atm/cm; 100 ItS marker. I atm ~ 101 kN/m 2.
(facing p. 446)
DYNAMIC CALIBRATION AT HIGtt SPL
I I I "~L200 ~ + 0 "; ,oo
0
447
I I
I
I
I
I
2
3
4
v" ( m / s )
Figure 4. The time to reach 89 maximum signal level,~, rersus the averagepiston velocity,~. Piston movement: o, 2.02 ram; +,. 3.84 ram. The average estimated error is given by:q'.
5. CONCLUSIONS From the experiments conducted it has been shown that pressure pulses suitable for dynamic calibration at high sound pressure levels may be produced by using the classical, impulsively moved piston. The apparatus described would allow calibration to be performed at varying angles of incidence to the transducer diaphragm. It should be possible, by using piston damping and other means, to shape the calibration pulse to correspond to the pulses whose measurement is sought. The apparatus described here is in its simplest form and may be considerably improved by independent piston velocity measurement and more convenient methods of actuating the secondary piston.
REFERENCES 1. J. J. VAN HOUTEN and R. BROWN 1968 N A S A CR-1075. Investigation of the calibration of microphones for sonic boom measurements. 2. R. O. GOODCHILDand L. BERNSTEIN1973 Aeronautical Research Cou,cil CP No. 1240. On the calibration of pressure transducers for use in shock tunnels.
A TECHNIQUE FOR THE DYNAMIC CALIBRATION OF MICROPHONES AND PRESSURE TRANSDUCERS AT HIGH SOUND PRESSURE LEVELS D. JONES Hawker Siddeley Dynamics, Hatfield, England AND
T. V. JONES
Department of Engh~eerhlg Science, University of Oxford, Oxford OX1 3PJ, England
(Received 28 August 1973) A technique is described which enables microphones and pressure transducers to be dynamically tested at the sound pressure levels currently experienced in some vehicle and industrial environments. This employs a piston which is moved impulsively in a tube and generates a pressure pulse of calculable magnitude. Experimental results are presented which confirm that pressure pulses of the magnitude expected by theory are produced. I. INTRODUCTION High sound pressures of order 1 Ibf/in2t r.m.s. (~171 dB SPL) are of concern in some vehicle and industrial environments. The environments may be transient, as in the case of sonic booms, or sustained, as in the case of noise associated with powerful motors. To ensure accurate measurement of such fields methods of calibration of pressure transducers at high dynamic pressures are necessary. The calibration techniques currently in use have been summarized in references [1] and [2], where it can be seen that the shock tube is a primary technique commonly used at high pressures. However, in the case of microphones, calibration at atmospheric pressure is often necessary and hence a very weak shock wave is required. The pressure rise across a weak shock wave depends on the difference between the shock velocity and that of sound and as the measured quantity is the shock wave velocity the errors in determining the pressure rise may be large [2]. In the apparatus described here a pressure pulse similar to that in a shock tube was produced; however, it was generated by moving a piston impulsively in a tube and not by bursting a diaphragm. The magnitude of the pressure pulse was linearly related to the piston velocity in the acoustic approximation and this velocity was measured. In the following a description of the apparatus and the results obtained are given. The experiment was conducted in order to test the feasibility of the device and the resulting pressure pulses were measured by using a commercially available piezo-electric pressure transducer mounted in the reflecting end wall of the tube. The results obtained demonstrated that the method provides a simple means of dynamic calibration at high sound pressure levels. t l lbf/in2 ~ 6.9 kN/m2. 443
444
D. JONESAND T. V. JONES 2. THEORY
In a weak pressure wave the increase, p, above the ambient pressure, P, may be related to the flow velocity, v, by +
+ ...,
(])
where c is the ambient velocity of sound. On reflection from a rigid wall the pressure at the wall, Pa, is given by +....
(2)
In the acoustic limit v ~ c and equation (2) becomes PR -
P -
2Vv =
(3)
c
For the case considered here of a piston in a tube, where the piston accelerates over a short period and then decelerates slowly and is finally brought to a sudden halt, the variation of pressure at the reflecting wall is shown in Figure 1. This may be described in general by the equation (4) /'I=0
ILIIL"
(o) 0
b
C
(b)
(c)
p. I
!
t
|
I
Figure I. (a) Schematic diagram of the experiment: a, piston; b, compression wave; c, pressure transducer. (b) Ideal piston velocity history, v v e r s u s t . (c) Pressure at the reflecting wall; - - . , multiple reflections; , single pulse due to limited piston motion.
DYNAMICCALIBRATIONAT HIGH SPL
445
where v(t) is the pistol velocity at time t and H(y) is the Heavyside function obeying H = 0 for y < 0 and H = 1 for y > 0. I is the distance between the piston and the reflecting wall, which is assumed to be constant. In the experiments to be described the piston was brought to rest soon after acceleration and hence the rarefaction resulting from this reached the reflecting wall before any reflections from the piston, giving the pressure as shown by the dotted line in Figure 1. This enabled the time during which the piston was moving to be found from the pressure at the reflecting wall, and hence the average piston velocity, as the piston movement was known.
3. APPARATUS The apparatus is shown in Figure 2. The 2.54 cm diameter tube was 60 cm long and mounted vertically, the piston being at its lower end. The latter was made of brass and was covered with a P.T.F.E. sleeve so as to be a close fit in the tube. The top of the tube was blanked off by a flange in which was mounted a Kistler 701S piezo-electric pressure transducer whose output was displayed on an oscilloscope. The piston motion was produced by allowing a secondary piston to strike a rod attached to the bottom of the piston although
Figure 2. A diagram of the apparatus: a, Kistler 701S; b, copper tube; c, rubber section; d, P.T.F.E. sleeve; e, piston; f, P.T.F.E. guide; g, spacer; h, P.T.F.E. block; i, solenoid; j, secondary piston; k, stop.
446
D. JONES AND T. V. JONES
the motion was limited to a few millimeters. The secondary piston movement was produced electromechanically by using a solenoid through which a capacitor bank was discharged. In this manner the piston motion was impulsive and velocities up to 5 ms -1 were achieved. Half-way along the tube was a short section of nitrile rubber which served the purpose of reducing the effect of mechanical vibrations travelling up the tube and producing spurious transducer signals. 4. R E S U L T S
Typical transducer output signals may be seen in Plate 1. In Plate l(a) is shown the "staircase" in pressure due to multiple reflections when the piston motion was not limited, whereas Plate l(b) shows the single pulse resulting when only a small piston movement was allowed. The single pulse results were those analysed in the experiment. From traces such as that shown in Plate l(b) the time during which the piston was in motion could be measured and as the piston movement was limited to a known distance the average piston velocity, ~, could be found. The average pressure within the pulse,/~R, was measured, the manufacturer's calibration checked at high pressure with a shock tube being used, and this is plotted against iri Figure 3 for two values of piston movement. As/~R is linearly related to o by the acoustic approximation (equation (3)) the following equation should hold" PR --
P
2~,~ =
(5)
c
This is plotted in Figure 3 where good agreement with the experimental results is shown. A measure of the rise time of the pressure pulse achieved in the experiments is shown in Figure 4, where the time to reach half of the plateau value is plotted v e r s u s the average piston velocity. As may be seen, rise times of order 100/ts are approached at high velocities.
I
I
I
I
/
x,r 4 9
I
.4-
-4-
+
3
2 o
I
0
Lf
I I
I 2
I $
I 4
I 5
~" ( m / s )
Figure 3. The average pressure rise at the reflecting wall,/~, v e r s u s the average piston velocity, t~, and a comparison with theory (equation (5)). Piston movement: o, 2.02 mm; +, 3-84 mm; , acoustic theory (equation (5)).
Plate 1. Typical reflected pressure outputs. (a) Multiple reflections; sensitivity, 4 x 10 -2 atm/cm; timebase, 5 ms/cm. (b) Single pulse; sensitivity, 10 -2 atm/cm; 100 ItS marker. I atm ~ 101 kN/m 2.
(facing p. 446)
DYNAMIC CALIBRATION AT HIGtt SPL
I I I "~L200 ~ + 0 "; ,oo
0
447
I I
I
I
I
I
2
3
4
v" ( m / s )
Figure 4. The time to reach 89 maximum signal level,~, rersus the averagepiston velocity,~. Piston movement: o, 2.02 ram; +,. 3.84 ram. The average estimated error is given by:q'.
5. CONCLUSIONS From the experiments conducted it has been shown that pressure pulses suitable for dynamic calibration at high sound pressure levels may be produced by using the classical, impulsively moved piston. The apparatus described would allow calibration to be performed at varying angles of incidence to the transducer diaphragm. It should be possible, by using piston damping and other means, to shape the calibration pulse to correspond to the pulses whose measurement is sought. The apparatus described here is in its simplest form and may be considerably improved by independent piston velocity measurement and more convenient methods of actuating the secondary piston.
REFERENCES 1. J. J. VAN HOUTEN and R. BROWN 1968 N A S A CR-1075. Investigation of the calibration of microphones for sonic boom measurements. 2. R. O. GOODCHILDand L. BERNSTEIN1973 Aeronautical Research Cou,cil CP No. 1240. On the calibration of pressure transducers for use in shock tunnels.