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2.4 Acoustics2.4.1 The speed and attenuation of soundGases and vapours The attenuation of plane sound waves in neper/unit length is α = (l/2d)ln(I0/Id), where the initial intensity I0, has decreased to Id after traversing distance d. When expressed in decibels per unit length, convenient for practical application, the value is 8.686α. In normal monatomic gases α varies classically as f 2, f being the frequency, but in polyatomic gases relaxation phenomena may dominate over classical absorption. (See Herzfeld and Litovitz, 1959.) For gases at moderate pressure the speed of sound c = √(γp/ρ) or alternatively c = √/(γRT/M), p being the ambient gas pressure, γ the ratio of the specific heat at constant pressure to that at constant volume, R the gas constant, T the absolute temperature and M the molecular weight. Thus, to first order, c is proportional to √T and is independent of gas pressure; at higher pressures, however, the value is changed due to contributions from the second and higher virial coefficients. The speed of sound waves bounded by walls or tubes is less than the free-space value. Dispersion is observed for sound propagation in many polyatomic gases due to molecular relaxation: above the relaxation frequency the rotational or vibrational degrees of freedom are not excited, the specific heats are modified and the speed of sound is increased. The table below gives experimentally determined values of sound speed in gases and vapours, selected from the literature. Where known, both the low-frequency and high-frequency limiting values are given, the latter being in brackets. Speed of sound in gases and vapours
Attenuation of sound in air The attenuation of sound in air due to viscous, thermal and rotational loss mechanisms is simply proportional to f 2. However, losses due to vibrational relaxation of oxygen molecules are generally much greater than those due to the classical processes, and the attenuation of sound varies significantly with temperature, water-vapour content and frequency. A method for calculating the absorption at a given temperature, humidity, and pressure can be found in ISO 9613-1 (1993). The table gives values of attenuation in dB km−1 for a temperature of 20°C and a pressure of 101.325 kPa. The uncertainty is estimated to be ± 10%. Attenuation of sound in air (dB km−1)
Speed of sound in air The speed of free progressive sound waves in standard dry air containing 0.03% CO2 by volume is 331.46 ± 0.10 m s−1 at a temperature of 0°C and a pressure of 101.325 kPa (see Cramer, 1993). The speed of sound in air changes with temperature, water vapour content, and CO2 content. The table gives values of the speed in m s−1 for a range of temperatures and humidities at 0.03% CO2 by volume. The uncertainty in the values in the table is estimated to be 0.1 m s−1.
Speed, attenuation and non-linearity of sound in liquids The speed of dilatational waves in unbounded fluids is c = (βaρ)−1/2, βa being the adiabatic compressibility and ρ the density. In practice the propagation velocity of each part of a sound wave depends on the local amplitude and the importance of this effect is determined by the ratio B/A = (ρ/c2)∂2p/∂ρ2 (where p is the pressure and all quantities are at ambient pressures and constant entropy). For plane waves the sound speed is then c + βu, where u is the particle velocity and β = 1 + B/2A (see Hamilton and Blackstock, 1988). In normal fluids the classical attenuation is proportional to f 2, f being the frequency, but relaxation phenomena may dominate; the attenuation generally decreases with increasing temperature. Values for various liquids are given below, selected from numerous sources; f is in Hz and α is in neper m−1. Where known, the frequency at which the attenuation was measured is given in brackets, in MHz. The temperature for the B/A values is given in brackets, in °C. Properties of sound in liquids
* The acoustic properties of helium are highly complex and dependent on temperature; see Rudnick (1980). Acoustic properties of distilled water Air-free distilled water is non-dispersive but the temperature dependence of sound speed is anomalous, mainly because of the temperature dependence of the adiabatic compressibility of the water molecule itself; the maximum speed occurs at a temperature of approximately 74.16 °C. The pressure coefficient is approximately + 0.156 m s−1 atm−1at 20 °C (see Del Grosso and Mader, 1972, Chen and Millero, 1976, Bilaniuk and Wong, 1993). The estimated uncertainty in the tabulated values is less than ± 0.02 m s−1. The attenuation of sound in distilled water is | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
