Analog model for thermoviscous propagation in a cylindrical tube.

Modeling acoustic propagation in tubes including the effects of thermoviscous losses at the tube walls is important in applications such as thermoacoustics, hearing aids, and wind musical instruments. Frequency dependent impedances for a tube transmission line model in terms of the so-called thermal and viscous functions are well established, and form the basis for frequency domain analysis of systems that include tubes. However, frequency domain models cannot be used for systems in which significant nonlinearities are important, as is the case with the pressure-flow relationship through the reed in a woodwind instrument. This paper describes a cylindrical tube model based on a continued fraction expansion of the thermal and viscous functions. The model can be represented as an analog circuit model which allows its use in time domain system modeling. This model avoids problems with fractional derivatives in the time domain.

Performance of tonpilz transducers with segmented piezoelectric stacks using materials with high electromechanical coupling coefficient.

Tonpilz acoustic transducers for use underwater often include a stack of piezoelectric material pieces polarized along the length of the stack and having alternating polarity. The pieces are interspersed with electrodes, bonded together, and electrically connected in parallel. The stack is normally much shorter than a quarter wavelength at the fundamental resonance frequency so that the mechanical behavior of the transducer is not affected by the segmentation. When the transducer bandwidth is less than a half octave, as has conventionally been the case, for example, with lead zirconate titanate (PZT) material, stack segmentation has no significant effect on the mechanical behavior of the device in its normal operating band near the fundamental resonance. However, when a high coupling coefficient material such as lead magnesium niobate-lead titanate (PMN-PT) is used to achieve a wider bandwidth with the tonpilz, the performance difference between a segmented stack and a similar piezoelectric section with electrodes only at the two ends can be significant. This paper investigates the effects of stack segmentation on the performance of wideband underwater tonpilz acoustic transducers. Included is a discussion of a particular tonpilz transducer design using single crystal piezoelectric material with high coupling coefficient compared with a similar design using more traditional PZT ceramics.

Thermal boundary layer effects on the acoustical impedance of enclosures and consequences for acoustical sensing devices.

Expressions are derived for the acoustical impedance of a rectangular enclosure and of a finite annular cylindrical enclosure. The derivation is valid throughout the frequency range in which all dimensions of the enclosure are much less than the wavelength. The results are valid throughout the range from adiabatic to isothermal conditions in the enclosure. The effect is equivalent to placing an additional, frequency-dependent complex impedance in parallel with the adiabatic compliance. As the thermal boundary layer grows to fill the cavity, the reactive part of the impedance varies smoothly from the adiabatic value to the isothermal value. In some microphones, this change in cavity stiffness is sufficient to modify the sensitivity. The resistive part of the additional cavity impedance varies as the inverse square root of frequency at high frequencies where the boundary layer has not grown to fill the enclosure. The thermal modification gives rise to a thermal noise whose spectral density varies asymptotically as l/f(3/2) above the isothermal transition frequency.

Noise in miniature microphones.

The internal noise spectrum in miniature electret microphones of the type used in the manufacture of hearing aids is measured. An analogous circuit model of the microphone is empirically fit to the measured data and used to determine the important sources of noise within the microphone. The dominant noise source is found to depend on the frequency. Below 40 Hz and above 9 kHz, the dominant source is electrical noise from the amplifier circuit needed to buffer the electrical signal from the microphone diaphragm. Between approximately 40 Hz and 1 kHz, the dominant source is thermal noise originating in the acoustic flow resistance of the small hole pierced in the diaphragm to equalize barometric pressure. Between approximately 1 kHz and 9 kHz, the noise originates in the acoustic flow resistances of sound entering the microphone and propagating to the diaphragm. To further reduce the microphone internal noise in the audio band requires attacking these sources. A prototype microphone having reduced acoustical noise is measured and discussed.