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Fig. 2. Frequency dependence of the characteristic acoustic impedances of the atmospheres considered. The choice of acoustic emitters and receivers for the dif- ferent environments must be such that the impedance of the transducer is matched to that of the respective medium. Thus, piezoelectric materials would be good can- didates for Venus and possibly Titan, while for Earth but most critically for Mars, electrostatic capacitive transducers should be used to ensure the best coupling.
Fig. 1. (a) Frequency dependence of the acoustic attenuation coefficient α and nor- malized attenuation αλ. The peaks in αλ indicate more readily the effective relax- ation frequencies, which are directly related to the molecular relaxation times. (b) Frequency dependence of sound speed c on the planets’ surfaces. Over the fre- quency range considered, the attenuation on CO2–dominated Mars is the largest while Titan’s is the smallest. Due to the extremely hot Venusian environment, relax- ational effects extend into the MHz range, as indicated by the two inflection points in both the attenuation and (less visible) sound speed. Even though the main con- stituents of Mars and Venus are the same (and in comparable concentrations), Venus’ high temperature makes its environment acoustically the “fastest,” while Titan’s cold atmosphere is the “slowest.”
particle velocity. For the ideal case of plane waves, a pressure fluctuation produces an in-phase particle velocity, which makes the acoustic impedance real and equal to the product between the ambient density ρ0 and the sound speed in the medium c. The plane-wave Za for the four planets is shown in Fig. 2. The impedance appears flat over the frequency range for Mars, Earth, and Titan due to the vertical scale chosen in the graph (the frequency dependence of Za is imposed by that of the sound speed c). A slight inflexion point in Za is appar- ent for Venus at ~ 1 MHz. Earth and Mars are the least “acoustically responsive,” with Zac of 407 and 4.4 kg/m2s, respectively. Considerably higher acoustic impedances char- acterize the high-pressure environments of Titan and Venus: on Titan, Zac = 5738 kg/m2s and on Venus, Zac = 26,687 kg/m2s. Compared to Earth, the intensity of a sound wave would be 20 dB weaker on Mars, and 12 dB and 18 dB stronger on Titan and Venus, respectively (if produced by the same source and not accounting for absorption).
Typically, the acoustic impedance of an elastic solid and that of a gas differ by several orders of magnitude. For exam- ple, Zac for piezoelectric crystals or ceramics is about 107 kg/m2s, compared to water with Zac ~1.5 x 105 kg/m2s and air at normal conditions with Zac ~ 400 kg/m2s. Therefore, a stress wave generated in the piezoelectric solid is only partially trans- mitted as a pressure wave in the fluid. Thus, in active acoustic sensors (i.e. incorporating an emitter-receiver path) this impedance mismatch can drastically reduce the sensing effi- ciency as acoustic waves are launched in the gas by piezoelec- tric emitters. For applications such as acoustic anemometry requiring frequencies of tens of kHz, a promising transducer choice for the tenuous Martian environment is low-impedance (Zac on the order of 1000 kg/m2s), microfabricated, air-gap, capacitive devices that can provide much better acoustic cou- pling to a tenuous environment and are capable of dynamic
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ranges in excess of 100 dB.
An alternative may be the recent-
ly reported optically diffractive capacitive ultrasonic transduc-
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ers with improved detection sensitivity. The considerably
surface temperature, the environment of Venus is acoustical- ly the “fastest” while Titan’s atmosphere is the “slowest.” Even though the overall atmospheric compositions of Mars and Venus are similar, the large difference in temperatures plays a crucial role for the sound speeds. From the point of view of instrument development, the different wave propagation speeds dictate not only the lengths of transmitter-receiver paths in sound speed sensors, but also the data acquisition timing requirements, which are critical in setting the resolu- tion of sound speed measurements.
Acoustic impedance and transducer choice
Perhaps the most important quantity to consider at the outset when developing acoustic sensors is the medium’s characteristic acoustic impedance, Zac, defined as the ratio of the instantaneous (acoustic) pressure p and particle velocity u, Zac, ≡ p/u , with units of 1 kg/m2s or 1 Rayl. The character- istic acoustic impedance is generally complex-valued due to a phase difference between the instantaneous pressure and
Alien Soundscapes 19