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Extending the frequency range of PTB's sound pressure standard down to
2 Hz for the traceability of acoustic measurements in the infrasonic range


The primary calibration in the pressure chamber provides the most precise procedure for the realization of the sound pressure unit to date. In order to realize this unit with the highest possible accuracy, the reciprocity procedure is used to calibrate highly stable, standardized condenser microphones, the so-called "laboratory standard microphones". They are characterized by their combining a large frequency and dynamic range with a relatively low influence of the ambient conditions (static pressure, temperature and ambient humidity) on their sensitivity and high time-dependent stability.

This relies on the fact that such condenser microphones are reversible reciprocal two-terminal networks. This means that not only do they, as usual when subjected to a sound pressure, generate an output voltage, but they can also generate a volume velocity when fed by an alternating current.

For the reciprocity calibration, three microphones (M1, M2 and M3) are used with the sensitivities M1(f), M2(f) and M3(f) which depend on the frequency f. Two of them at a time are acoustically coupled with each other in a precisely defined manner, namely in such a way that each of the three microphones acts once as a transmitter and once as a receiver.

For each pair, the current Is flowing through the transmitting microphone and the open-circuit output voltage of the receiver microphone Ue are measured as a function of the frequency. The quotient Is/Ue is referred to as the electrical transfer impedance. It describes the input/output behaviour of the system consisting of the two microphones and the acoustic coupling.

The acoustic coupling of the microphones is realized via cylindrical couplers of very precisely known dimensions (see Figs. 1 and 2). To determine the so-called "acoustic transfer impedance", the physical properties of the coupling medium "air" must also be known; these, in turn, depend on the temperature, the relative humidity and the static pressure and must be precisely determined and taken into account. A plane sound wave propagates inside the coupler as long as the coupler diameter (which corresponds to the diameter of the microphone's diaphragm) is small compared to the sound wavelength. The acoustic transfer impedance of the microphone/coupler/microphone system can be represented as a homogeneous transmission line which is terminated by the acoustic impedances of the two microphones. The parameters of the transmission line are first, the dimensions of the coupler and of the microphones. They are secondly, the properties of the enclosed air, which depend on the ambient conditions, and thirdly, the acoustic impedances of the microphones mentioned earlier. To calculate the latter precisely, a fitting procedure is used where the differences in the measurement results in couplers of different lengths serve as a basis.

The sensitivities M1(f), M2(f) and M3(f) of the three microphones are calculated from the frequency-dependent electrical and acoustic transfer impedances. In the case of medium frequencies (125 Hz to 4 500 Hz), a measurement uncertainty of 0.03 dB
(k = 2) is achieved; towards high frequencies (10 kHz), the measurement uncertainty increases to reach up to 0.08 dB.

To attain such low uncertainty, it is necessary to quantify and correct numerous effects such as the heat conduction through the walls of the coupler cavities or the formation of radial modes inside the coupler. The values determined for the open-circuit pressure sensitivity are given for the reference ambient conditions (temperature, static air pressure and relative humidity) and are then stated as open-circuit pressure sensitivity levels in dB (re 1 V/Pa).

Until recently, calibration took place in the audio frequency range, i.e. from 32 Hz to 10 kHz. The frequency range has recently been extended down to 2 Hz at PTB; this will make the highly demanded traceability of sound measurements in the infrasonic range possible soon. The particular challenges at such low frequencies consist in forming a microphone/coupler/microphone system that is sufficiently airtight, which often requires the microphone front surfaces to be mechanically post-processed. Moreover, the transition from the adiabatic to the isothermal behaviour of the coupling medium "air" must be taken into account adequately. This enabled a measurement uncertainty (k = 2) of 0.12 dB to be achieved at up to 4 Hz and a measurement uncertainty of 0.23 dB to be attained for even lower frequencies up to 2 Hz.

A EURAMET interlaboratory comparison including this frequency range will soon be completed.

 Figure 1: Two laboratory standard microphones (top) with a coupler (bottom left) for the reciprocity calibration. The coupling volume is formed by the inner cylinder barrel and the two microphone membranes (see also Fig. 2). A capillary is affixed to the coupler for pressure equalization with the ambient air pressure; this capillary can be sealed during measurements by means of a loosely fitting needle with a handle (bottom right).


Figure 2: Microphones and coupler from Fig. 1 in their usual position (left); mounted into an enclosing housing, ready for the measurement of the electric transfer impedance (right).


Contact person:

Thomas Fedtke, FB 1.6, AG 1.61, E-Mail: Opens window for sending emailThomas.Fedtke(at)ptb.de