Propagation of Sound Through Atmospheric Fog

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  • 1 Div. of Engineering, Brown University, Providence, R. I.
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Abstract

The propagation of sound in an atmospheric fog is described by considering a system of liquid droplets suspended in a mixture of their vapor and a noncondensing gas. The perturbation of this system by a sound field causes the droplets to exchange mass, momentum and beat with the surrounding gaseous mixture, and results in acoustic attenuation and dispersion. For low mass concentrations of liquid phase, the Napier frequency (τ¯ = 1, when attenuation per unit wavelength is a maximum) is expressed in terms of f τ¯ = ωτt/Cm, where Cm is the liquid mass fraction and τt is, for example, the thermal relaxation time. For an infinite Lewis number (ratio of thermal diffusivity to mass diffusivity) the results reduce to published expressions for nonvolatile particles. Strong attenuation per unit wavelength due to mass transfer effects is predicted in the sub-audible (infrasonic) region in which signals from weather fronts and atmospheric explosions are monitored.

Dimensional attenuation is found to be nearly constant both for infrasonic and low audible frequencies where ω ≤ 1/τt(e.g., for a warm air fog of droplets with an 8 μm radius, ω = 2ϕf ≤ 1200 sec−1) and for high frequencies where ω ≥ 1/τt. The level of dimensional attenuation for the high frequencies is approximately six times that at the low-frequency level. Transition from the low level to the high level of attenuation depends on fog particle size through the relation, ωτt = 1. Computed results for typical fog data are given, and optimal signaling frequencies are discussed.

Abstract

The propagation of sound in an atmospheric fog is described by considering a system of liquid droplets suspended in a mixture of their vapor and a noncondensing gas. The perturbation of this system by a sound field causes the droplets to exchange mass, momentum and beat with the surrounding gaseous mixture, and results in acoustic attenuation and dispersion. For low mass concentrations of liquid phase, the Napier frequency (τ¯ = 1, when attenuation per unit wavelength is a maximum) is expressed in terms of f τ¯ = ωτt/Cm, where Cm is the liquid mass fraction and τt is, for example, the thermal relaxation time. For an infinite Lewis number (ratio of thermal diffusivity to mass diffusivity) the results reduce to published expressions for nonvolatile particles. Strong attenuation per unit wavelength due to mass transfer effects is predicted in the sub-audible (infrasonic) region in which signals from weather fronts and atmospheric explosions are monitored.

Dimensional attenuation is found to be nearly constant both for infrasonic and low audible frequencies where ω ≤ 1/τt(e.g., for a warm air fog of droplets with an 8 μm radius, ω = 2ϕf ≤ 1200 sec−1) and for high frequencies where ω ≥ 1/τt. The level of dimensional attenuation for the high frequencies is approximately six times that at the low-frequency level. Transition from the low level to the high level of attenuation depends on fog particle size through the relation, ωτt = 1. Computed results for typical fog data are given, and optimal signaling frequencies are discussed.

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