Microphones respond to sound waves over a broad frequency range with a less than ideal output voltage. For scientific studies, we must determine the actual microphone response in order to correct the data to represent the true sound levels. Considering that aircraft flight certification regulations (FAR Part 36) include frequencies up to 10 kHz, aero acoustic measurements at frequencies above 40 kHz are frequently required because aero acoustic researchers will of-ten use scale models to simulate noise generated by a large device or vehicle.
For example, the large size and operational expense of commercial transport aircraft make it imperative to perform most aircraft noise experiments with small-scale aircraft models. The acoustic frequency of aircraft model noise is inversely related to that of the full size aircraft by the linear scale of the model such as wing span. The noise created by a 1110th scale model at 10 kHz corre-sponds to the noise created by the real aircraft at 1 kHz.
There are three microphone-related effects that need to be accounted for in order to correct the microphone signal to true sound level:
1) free-field response - the ratio of microphone output voltage to sound pres-sure that exists with the microphone in free field after correcting for the in-fluence of the microphone body on the acoustic field
The free-field response is determined by:
a) pressure response - the ratio of microphone output voltage to an un-steady pressure uniformly applied over the diaphragm
b) free-field correction - the amplification of the sound pressure at the diaphragm by interference and diffraction of the sound field
2) directionality of the microphone with and without grid or aerodynamic forebody
3) attenuation of the acoustic waves by the aerodynamic forebody
There are two basic types of condenser microphones in common use: free-field and pressure microphones.
Free-Field Response
The free-field microphone, as its name suggests, is designed for use in an open space. Because microphone housings cause interference and diffraction of sound waves with wavelengths comparable or smaller than the housing diam-eter, the acoustic pressure will be amplified at high frequencies. To compensate for this free-field effect, free-field microphones are constructed with internal damping of the diaphragm that approximately cancels the pressure amplifica-tion. The result is a flat frequency response, more or less, for sound waves propagating at normal incidence to the diaphragm. Other factors affecting mi-crophone choice include accuracy requirements, anticipated noise levels, fre-quency range, and environmental conditions. Taniguchi and Rasmussen
(1979) describe a microphone selection procedure for engine and aircraft noise measurements.
Knowing the free-field response allows correction of acoustic data to true sound levels over the frequency range of the instrumentation. At low frequen-cies, a high quality microphone will have a flat response with frequency. In that case, a simple pistonphone or similar field calibrator can be used to adjust the signal for true sound level. This procedure corrects for microphone sensitiv-ity. At high frequencies the microphone free-field response will not be flat, and steps must be taken to determine the variation with frequency and the corre-sponding data corrections.
Pressure Response
Pressure response microphones are designed to mount flush in a wall and, in this configuration, do not have a free-field effect other than pressure doubling at the wall caused by superposition of the incident and reflected waves. The micro-phone response is thereby optimized for sound waves striking the wall. Each di-aphragm and preamplifier with associated electronics in the data acquisition system has a unique response to an oscillating pressure applied to the di-aphragm. The pressure response of a microphone (free-field or pressure re-sponse) is typically measured in calibration laboratories to avoid the free-field amplification. Calibrations can be made by the electrostatic actuator method or by use of an acoustic reciprocity method (Frederiksen and Christensen 1998).
The electrostatic actuator method (Briiel and Kjaer 1982) imposes an oscil-lating electric charge to the bare diaphragm that simulates an acoustic pres-sure oscillation. The actuator input voltage is also used as the reference to eval-uate the microphone output. By sweeping through the desired frequency range, the following transfer function between input and output is found.
(1.41) where Gxy is the cross spectrum of the electrostatic actuator input voltage and the microphone output voltage, and Gxx is the auto spectrum of the actuator voltage. The pressure response in decibels is.
HPR(f) = 20 10glO
I
H(f)I
(1.42)where
I
H (f)I
is the magnitude of the transfer function, or gain factor of H (f) . A perfect microphone would have the same linear response to the input sig-nal at all frequencies, in which caseI
H (f)I
would be a constant. In practice, IH(f) I varies with frequency.The individual diaphragm dominates the system pressure response, which is influenced to a lesser degree by the electronics and cabling of each channel
in the data acquisition system. When long microphone cabling is used for very high frequency measurements, it is best to perform the electrostatic calibra-tion in-situ with the equipment to be used in the experiment. High frequency signal attenuation by cabling can be as high as 2 dB (Allen et al. 1995).
The sensitivity (pistonphone) field calibrations discussed above are also pressure response measurements (as opposed to measurements of freely prop-agating acoustic waves). Thus, it is advantageous to normalize the pressure re-sponse curves by setting their magnitudes to zero at the pistonphone calibra-tion frequency. This allows the pressure response correccalibra-tions to be applied separately from the sensitivity calibrations.
Figure 1.26 shows pressure response correction curves to 100 kHz mea-sured from many different microphone channels during a 40 x 80 in-situ elec-trostatic calibration. The differences between channels are as much as 5 dB, which demonstrates the need for calibrating each channel individually. The 61-m long signal cables between microphones and power supply/amplifiers carried the weak preamplifier voltages, pressure response was reduced 1- 2 dB above 50 kHz. Locating the power supply/amplifiers closer to the microphones alleviates the line loss.
In addition to the in-situ calibrations, all of the diaphragms including spares should be calibrated on a common preamplifier in the laboratory so that diaphragms can be replaced or exchanged during the test. This is some-times necessary if diaphragms are damaged or accumulate moisture from the air.
2 0 -2
~ -4
"0
i"
~ -6-8 -10
-12 0 20 40 60 80 100
frequency, kHz (M = 187 Hz)
Fig. 1.26. In-situ pressure response measurements of several microphone channels used in a wind tunnel experiment (B&K 4135 6.35 mm diameter condenser microphones) (Allen et al. 1995)
To substitute microphone diaphragms for those used during the in-situ pressure response calibrations, the following procedure is used. The pressure response correction for the ith microphone channel and the jth diaphragm is determined from the following equation,
(1.43) where HPRik is the pressure response curve of the ith microphone channel in-situ calibration using the kth microphone diaphragm, and HPRlabk and HpRlilbj are the pressure response curves obtained in the laboratory with the kth and jth di-aphragms, respectively, mounted to common power supply/amplifiers. All re-sponse curves are normalized to 0 dB at the pistonphone frequency, e. g., 250 Hz.
Free-Field Correction
As mentioned above, a microphone placed in an acoustic field will generate in-terference and diffraction of the sound waves, which causes a higher pressure at the diaphragm than would be measured by a nonintrusive instrument. The pressure increase is particularly pronounced for sound waves that arrive per-pendicular to the diaphragm (zero or normal incidence) and have wave-lengths equal to or less than the microphone diameter.
The free-field correction is usually measured in a laboratory using an acoustic reciprocity method (lEC 1995). Juhl (1994) developed a numerical method to predict the same effect. The magnitude of the free-field correction for a B&K 4135 6.35 mm diameter free-field microphone (bare diaphragm at normal incidence) as a function of frequency has been measured and pub-lished in the B&K microphone users manuals (Briiel and Kjaer 1971, 1982).A curve fit of this correction is given by the polynomial:
Hpp(j)
=
0.46888 - {1.3249 X 1O-4)f+ (2.8876 X 10-8)
J2 -
(9.0321 X 10-13)P
+ {1.2855 X 1O-17)j4 -{1.0181 X 1O-22)j5 + (4.8886 X 10-28) j6 - (1.4977 X 10-33 )
r
+ (2.9289 X 10-39)
JB -
(2.9285 X 10-45)r
(1.44)where fis the frequency. A plot of the B&K free-field correction and curve fit of Equation 1.44 is shown in Figure 1.27.
When combined, the pressure response and free-field correction functions determine the free-field response correction, HpR , of a microphone channel to freely propagating sound waves.
(1.45) Figure 1.28 shows a B&K 4135 microphone pressure response curve (lower), field correction curve (upper) from Figure 1.26 and the resulting
free-10
- - curve fit 8
r:Q 6
"0
&..
p:f 4
2
0 0 20 40 60 80 100
frequency, kHz
Fig. 1.27. B&K microphone free-field correction (Brtiel and Kjaer 1982) and curve fit
10
5
... -... ----...
_-
...,... . ... .
.... -"'--.
","
---•••••••••••••••••••• ; , ... M ... H ... N ... N •••••••••••••••••••••••••••••
---HFF --HFR 0 ... --+-HpR
r:Q "0
::rf -5
-10
-15 0 20 40 60 80 100
frequency, kHz (oM = 187 Hz)
Fig. 1.28. Typical B&K 4135 pressure response curve (lower), which when combined with a free-field effect curve (top) result in a free-field response curve (middle). Sound waves are normally incident to the diaphragm. Microphone diameter is 6.35 mm (Allen et al. 1995)
field response curve (middle). The deviation of the free-field response from 0 dB is on the order of 5 dB at 100 kHz, and could be used to correct data to true sound levels. This is an example of a free-field microphone that has a pressure response designed to almost cancel the free-field effect.
Microphone Directional Response
The free-field correction and resulting free-field response curves of Figure 1.28 change with angle of acoustic incidence. If available, corrections provided by microphone manufacturers can be used to correct for directionality effects.
If not available, or when making very high frequency acoustic measurements, it is best to use microphones with a bare diaphragm pointed directly at the source of interest (normal incidence). Complications induced by the grid or foam ball, and directivity effects are thereby obviated.
Aerodynamic Microphone Forebody Frequency Response and Directivity Pointing the microphone at the source is rarely possible with in-airstream measurements in wind tunnels because forebodies must point into the wind.
Special corrections for forebody effects on free-field response and directivity are therefore required. Unless provided by the manufacturer, calibrations such as described below must be performed.
Because the forebody affects the directional and free-field response of the microphone, the combined effects must be accounted for. The following pro-cedure accounts for both effects 2 and 3 discussed at the start of this section.
The photograph of Figure 1.29 shows a setup for measuring the aerody-namic microphone forebody (AMF) frequency response corrections and di-rectivity effects. The measurements are performed in an anechoic chamber to prevent reflections from contaminating the data. An impinging jet pneumatic source (Soderman et al. 2000) shown near the researcher generates broadband sound over the frequency range from 5 to 100 kHz.
Three microphone configurations are used to perform the AMF calibration:
1) A microphone with forebody rotates around the diaphragm position in the horizontal plane. 2) The same microphone without forebody is aimed at the noise source for the baseline configuration. The microphone does not rotate.
3) A reference microphone some distance away assures the stability of the noise source and indicates any spurious background noise intrusion.
The forebody free-field response gain factors
(1.46) are obtained as a function of frequency, f, and incidence angle,
e
defined in Figure 1.21 as the angle between the forebody long axis and wave normal.Fig. 1.29. Setup for the determination of aero-dynamic forebody and directivity correction in anechoic chamber. Forebody at top of photo is aimed at source and researcher. The vertical strut is wrapped with fiberglass
Gxx (f, 8) is the auto spectra of the test microphone signal, and Gyy (f, 0) is the auto spectra of the baseline microphone signal at normal incidence. By using the bare diaphragm, normal incidence signal as the baseline reference in Equa-tion 1.46, the transfer funcEqua-tions obtained during the anechoic chamber cali-bration contain only forebody effects on microphone response. These transfer functions are corrections that can be added to the microphone free-field re-sponse curves to find the frequency rere-sponse of the complete data channel:
cabling, power supply/amplifiers, microphone diaphragm, plus forebody.
Figure 1.30 shows the forebody transfer functions for many different FITE microphone forebodies at 90° incidence to the sound waves. The deviation from 0 dB is quite large at high frequencies and represents corrections that must be added to the microphone free-field response curves. There are signif-icant differences between the curves indicating that each microphone fore-body must be calibrated individually.
Figure 1.31 shows similar data for one FITE forebody plotted versus inci-dence angle at selected frequencies. Because data were obtained only from 0° to 180°, the curves from 180° to 360° are images of the measured data. At 60 kHz and below, the directivity effect is less than 5 dB. Above 60 kHz, the di-rectivity effect is as much as 8 dB. Since a desired accuracy of ± 1 dB is typical, the effect of forebody directivity on microphone response is important.
The azimuthal directional response of a forebody, i. e., directivity about the microphone long axis is more uniform than the longitudinal response below 90 kHz. However, the azimuthal directivity effect can be significant at some frequencies because of variations in forebody screen construction. It is
rec-5 0 -5
:l:l -10
"0
;...
~-15
:tF'
..: -20-25 -30 -35
0 20 40 60 80 100
frequency, kHz (M = 187 Hz)
Fig. 1.30. Microphone forebody free-field response for many different 6.35-mm diameter forebodies at 90° acoustic incidence angle (Allen et al.1995). The free-field response is sub-tracted from the data to arrive at true sound levels
90·
120· 60·
0
~ -10
'"0 ii. ::>;
<:
J
-20-30 O·
Fig. 1.31. Directional free-field response of a FITE forebody in the horizontal or longitudi-nal plane (Allen et al. 1995)
ommended that an azimuthal orientation be chosen during forebody calibra-tions, and that this orientation relative to the source be maintained when the forebodies are used for wind tunnel testing.
To apply the microphone forebody free-field response correction, HpRAMP' to test data the following equation is used:
Lp (f, 8) = Lpmeas (f, 8) - HpR (f) - HpRAMP(f, (J) (1.47) where 8 is the propagation angle (source-to-microphone) as illustrated in Figure 1.21
is the corrected sound pressure level, dB is the measured sound pressure level, dB
is the microphone free-field response correction at normal incidence, dB
H PR AMP (f, (J) is the forebody free-field response correction, dB
Strictly speaking, the accuracy in applying the microphone forebody correc-tions would be increased if the frequencies in the correction were adjusted to account for the temperature differences between the calibration and the test measurements. The forebody effects on microphone response depend on
fore-120.---.---.---.---.---.
Fig. 1.32. Application of microphone and forebody corrections to wind tunnel data (Allen et al. 1995)
body dimensions relative to the acoustic wavelength. If the temperature and consequently the speed of sound change, the acoustic wavelengths at each fre-quency will change. This effect on forebody response is small for small tem-perature differences.
Figure 1.32 shows the effect of the microphone and forebody corrections on measured data, which can be as much as 20 dB or more at very high frequen-cies. The microphone free-field response correction is the much smaller of the two corrections.
In many cases when measuring high frequency data, electrical tones may be evident in the spectra. These tones come from many sources including switch-ing power supplies used in computers and must be identified and removed from the narrow band spectra at the beginning of the data correction proce-dure. If necessary, background noise subtraction should also be applied early in the data process.
All the above corrections should be applied to narrow band data for the highest accuracy. Octave and third-octave results can be calculated from nar-row band data as necessary.