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THE SOUND OF MUSIC AND VOICES IN SPACE PART 2: MODELING AND SIMULATION
Timothy G. Leighton
Institute of Sound and Vibration Research, University of Southampton Highfield, Southampton SO17 1BJ, UK
and
Andi Petculescu
Department of Physics, University of Louisiana at Lafayette Lafayette, Louisiana 70504
As is shown in the paper, atmospheres affect both the generation and the propagation of sound. The effect on sound generation, depending on the actual source mechanisms that we exemplify by organ music and speech is two-pronged—the acoustic characteristics are altered not only by the nature of the gas but also by mass loading of the source. For the propagation of sound, the atmospheres act as frequency-dependent “filters,” characteristic of the com- position and ambient conditions of each planet.
Acoustic generation and fluid loading
The influence of an atmosphere on a sound source was studied based on two considerations. Firstly, both an organ pipe and the vocal cavity can be regarded as resonators. The resonance frequencies depend linearly on the sound speed in the gas in which they vibrate. Thus, at the outset (i.e., before propagating the waveforms), we adjusted the frequencies of the relevant features according to the predicted sound speeds for the atmospheres of Venus, Mars, and Titan (the pitch of the flue organ pipe scales with the sound speed, but for the voice only the frequencies associated with the vocal tract res- onances are scaled, leaving the voice pitch unaltered at this stage). Then, secondly, one considers the mass loading of the resonator by the surrounding atmosphere, which introduces an additional relative frequency shift calculated1,2 as
Here Δf is the actual frequency change, f0 is the reso- nance frequency in the absence of fluid loading, m is the inertial mass of the vibrating structure, and mrad is the cor- rection due to fluid loading, called the radiation mass. The results for the vocal tract of a child,2 show that a D (f = 293.66 Hz) at Earth’s surface is still an approximate D (f = 301.08 Hz) on Mars, but is shifted down close to a D# (f = 158.75 Hz) on Venus and close to a C # (f = 272.70 Hz) on Titan. Fluid loading influences speech much more than it does organ pipes. To emphasize the effect that mass loading has on the generation of sound by sources similar to the vocal cavity, we show speech samples before and after fluid loading was accounted for.
Acoustic propagation
The “filtering” effects of the different environments stud- ied (Earth, Mars, Titan, and Venus) on sound propagation
were simulated using a physical model of acoustic wave motion in multi-component gas mixtures. Combining ther- mo-viscous coupling and vibrational relaxation, the model predicts3 a frequency-dependent effective wave-number
from which the attenuation, α, and speed of sound, c, can be
computed at each frequency, respectively, as α = Im(keff)+ αclass
and c = 2πƒ /Re(keff), where αclass is the classical attenuation
coefficient due to thermal, viscous, and diffusional transport,
ρ0 and p0 are, respectively, the ambient density and pressure,
and Ceff and Ceff are the effective isobaric and isochoric specific PV
heats. The thermophysical quantities (e.g., specific heats, vis- cosity, and thermal conductivity) were interpolated at the ambient conditions (composition, pressure, and temperature)
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ofthesurfaceofeachplanet. Theatmosphericeffectonsound
propagation is to introduce selective attenuation and, to a smaller degree, dispersion, to the frequency content of the ini- tial waveform. As the waveform propagates, it is progressively altered by the atmospheric “filter.” These effects can be heard in the music files, which simulate how the Bach fragment behaves at various distances from the source.
Organization of the media files
The media files associated with the article are organized as follows. Table 1 sets the stage. Table 1 contains a calibra- tion tone at 97 dB re 2 μPa. A short clip of the organ solo (played on the organ in St. Margaret’s Church, East Wellow, Hampshire, United Kingdom), the words, Earth, Mars, Titan and Venus are then spoken and are used in the next three tables to illustrate how each might sound at the distances indicated and on each of the locations. The last example in Table 2 illustrates how all the organ clips would sound if played together. Note: If the sound becomes inaudible, it is due to the attenuation of the particular atmosphere. Do not continually adjust the volume to hear the sound.
Directions to download the interactive Tables and play the media files
Shortly after the print copy of this issue is mailed, it will also be published in the Acoustical Society of America’s Digital Library. The Acoustics Today main page can be found at http://scitation.aip.org/AT. Alternatively, the Table of
Sounds in Space 27