Two simple equations for the speed of sound in sea waters, down to depths of 4 km, have been obtained as approximations to a more precise equation developed by Lovett. The simpler of the two is valid for all Neptunian waters except the Red Sea, Mediterranean Sea, and Persian Gulf, and agrees with Lovett’s equation to within about 0.1 m/s. The other includes these water masses and is in agreement with Lovett to within about 0.03 m/s. The two equations are well adapted to programmable handheld calculators.
A perturbation expansion is formulated for the one-dimensional, nonlinear, acoustic-wave equation with dissipative term describing the viscous and thermal energy losses encountered in a rigid-walled, closed tube with large length-to-diameter ratio. The resulting set of iterative, linear equations is solved for a finite-amplitude standing wave. Solutions lead to a steady-state distribution of harmonics of the fundamental, the amplitude and phase of each term being strong functions of frequency and the absorptive process. Necessary features of the approach include characterizing all absorptive processes by a bulk absorption coefficient and requiring a boundary-layer depth much less than the tube diameter. The solution, while strictly limited to the preshock régime, can be used to predict certain features of the onset of shock. Intense longitudinal standing waves were generated within a rigid-walled tube of 6-ft length and 212-in. diam. The tube contained air, at ambient pressure and temperature, which was excited into vibration by a piston at one end. A microphone at the rigid end of the tube was used to observe the pressure as a function of time. For input frequencies around either the fundamental or the first overtone of the tube, the amplitudes of the second and third harmonics of the finite-amplitude wave were in excellent agreement with the predictions of the theory. Waveforms reconstructed from the predicted amplitudes and phase angles of the solution compared very well with the observed microphone output. An extension of the theory to the shock régime provided qualitative agreement with observations of the frequency dependence of both the intensity needed to produce shock and the phase of the onset of shock.
The sound velocity has been measured as a function of temperature and hydrostatic pressure for a number of organic liquids and for water-methanol mixtures. These data have been used to compute the ratio B/A of the coefficient B of the quadratic term to that of the linear term A in the adiabatic expansion of pressure changes in terms of density changes. The ratio has also been computed (by use of data from other sources) for sea water and for five alcohols. A discussion is given of various methods of computing B/A.
A three-dimensional mathematical model for acoustical standing waves in lossy fluid-filled cavities has been obtained which requires empirical values for the resonance frequencies fn and quality factors Qn (all measured in the linear acoustic r•gime) of the pertinent standing waves which the cavity can support. The nonlinear distortion of the observed pressure waveform depends strongly on the f's and Q's of those standing waves excited by harmonics of the driving frequency. The model is applicable to non-ideal cavities if the deviations from idealized geometry and boundary conditions are small. It is restricted to small values of M (1 q-1/2 B/A)Q•, where M is the peak Mach number and Q• the quality factor of the fundamental component of the driven standing wave, and B/A is the parameter of nonlinearity of the fluid. Comparisons between the model and experiment are made for a rectangular cavity driven in one-and twodimensional modes. Agreement is excellent except when there are degeneracies involving the predicted nonlinearly excited standing waves and other standing waves of the cavity. Small discrepancies appear to result from the coupling of energy from the nonlinearly excited standing wave into its degenerate neighbor. Subject Classification: 25.25; 55.20. liquid shear viscosity instantaneous and equilibrium densities of the flfiid velocity potential (angular) frequency at which the cavity is driven (angular) frequency of a resonance + 2 ß 1133
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