New primary standards for airborne infrasound – a Multiphysics approach
Conventionally, primary measurement standards for sound pressure are realised through calibration methods for the transducers and sensors used to measure sound pressure; microphones in the case of sound in air, though microbarometers are used widely for infrasound measurement.
Direct calibration methods where a known sound pressure is applied to the device under test, are often hindered by the circularity arising from the needing for a calibrated sensor to determine the applied sound pressure. Consequently, indirect methods have been developed exploiting the reciprocal nature of measurement microphones and used worldwide as the basis for establishing primary measurement standards. However, such methods have limitations at low frequencies. The current state-of-the-art capability cuts off around 2 Hz, whereas the Infra-AUV project targets frequencies that are orders of magnitude lower than this. Consequently, research in the project is seeking to extend reciprocity calibration further into the infrasound region of the frequency range. In developing new primary calibration capability, it is invaluable to have a means of validating results with some alternative independent calibration method, though this is usually quite rare in the field of metrology. It is then almost unprecedented that the Infra-AUV project is evaluating four further independent calibration methods in addition to developing reciprocity calibration.
Of all potential calibration methods, reciprocity calibration has been found to offer the best measurement uncertainty over the widest frequency range. It utilises three nominally identical microphones designed specifically for this purpose. Using one microphone as a sound source and the other to receive this sound, it is possible to determine the product of the sensitivities of the two microphones. Taking a third microphone and repeating the process with mutually exclusive pairings of microphones, enables the sensitivity of each individual microphone to be determined, all without the need to actually measure a sound pressure. The method requires the microphones to be coupled by a small sealed cavity, and this is where the low frequency limitations originate. Part of the method includes an analytical treatment of some acoustic characteristics of this cavity, but as the frequency reduces, there is a complex transition of the thermodynamic principles underlying these characteristics. Modelling this transition and the influence of inevitable sealing imperfections within the cavity are the two significant challenges being addressed in the project.
Reciprocity calibration was a solution to the difficulties in generating a known sound pressure without resorting to microphone measurements. However, when limiting the consideration to low frequencies, there are in fact some viable options.
A pistonphone is a device where a sealed cavity is driven by a piston. When the volume of the cavity and the volume change introduced by the piston are known, the adiabatic gas law enables the sound pressure to be calculated. Modern, so called laser pistonphones, use laser interferometry to determine the piston displacement that enables the sound pressure to be calculated when the piston geometry is known. If a microphone is then introduced into the cavity at the same time, a simple measurement of the output voltage is all that is needed to complete a calibration. Notice however, that physical basis for the calibration is the adiabatic gas law, which assumes that there is no heat exchange between the air and the walls of the cavity during the acoustic cycle.
In general, this is a valid assumption, but as the frequency is reduced, the increased period of the acoustic cycles allows more time for heat transfer to take place. Ultimately, full heat transfer will take place leading to isothermal changes. Therefore, calibration by a pistonphone in this transition region requires a model of the transition from adiabatic to isothermal conditions. This is in fact the same model needed for reciprocity calibration, and the significantly different cavity geometries provides a good basis for validating that model.
The pistonphone might also be referred to more generically as an infrasound generator. A potential alternative way of using the device is to use a water manometer in place of a laser interferometer, to determine the sound pressure generated by the piston. A water manometer is very simply, a U-tube partially filled with water. If one side is open to the atmosphere, and the other side connected to a source or pressure, there will be a difference in the water level in each arm of the U-tube, that corresponds to the acting pressure variation relative to the atmospheric pressure.
If that pressure is a sound pressure, the water column will oscillate and the magnitude of the oscillation, can be used to determine the acting sound pressure.
A slight adaptation of this principle is quite well known in underwater acoustics as a means of calibrating hydrophones. Here, instead detecting the pressure, the height of a water column acting on the transducer is varied to simulate a sound pressure where the magnitude is directly related to the variation in the height. The same principle can be used for microphones in air, except that the air column height, coming typically from the atmosphere, is not itself variable, but the position of the microphone within that air column can be altered. Therefore, applying a vertical sinusoidal displacement to the microphone will simulate a sound pressure by virtue of the variation in static pressure with height.
The final modality that is being investigated is the relationship between sound pressure and refractive index using a refractometer based on a Fabry-Pérot cavity. In a Fabry-Pérot cavity, two precision-aligned semi-reflecting mirrors face each other with reflecting faces towards the interior of the cavity separated by a given distance. A Fabry-Pérot refractometer can be described a resonant optical cavity that has regularly spaced resonance frequencies, the value of which depends on the refractive index of the medium. Their analysis therefore makes it possible to go back to the gas index in the refractometer with well-known equations like Edlén equation or others. Since the relationship between (sound) pressure and refractive index is well-modelled, the optical measurements lead to a determination of the sound pressure
Now, each of these methods are expected to work optimally over a relatively restricted range of frequencies. Part of the research is to evaluate the viability of each method, the measurement uncertainty, and the operable frequency range. However, the greatest strength comes from having so many alternative methods to consider. Collectively, these methods are anticipated to offer authoritative mutual validation and potentially provide an excellent basis for new primary calibration capability and traceability in the frequency range well below what is currently available.