![]() ![]() Rather, the part of the energy that has not yet been reflected maintains a spherical spreading law, which produces the gradual transition to a cylindrical surface at R→∞. To begin with, the transition from 20 log R to 15 log R to 10 log R is a continuous one, in that the surface of an expanding ray does not instantly become a cylinder once the ray encounters a boundary. However, these geometric arguments are oversimplifications, and depending on one's intended usage of the sonar equation, can lead to erroneous results. Based solely on geometric arguments (i.e., ducting by the waveguide surfaces), these intensity spreading laws fit easily into the sonar equation context, and one can see very nice examples worked out in Urick's text. Newhall, in Applied Underwater Acoustics, 2017 7.2.3.1 Simple Geometric Spreading Intensity ArgumentsĬommonly used (and abused) measures of acoustic propagation loss in shallow water are the geometrical spreading laws for sound intensity, i.e., the spherical, intermediate, and cylindrical spreading laws, often called the 20 log R, 15 log R, and 10 log R laws. However, although chaos theory is now well established, a physical (intuitive) understanding is still lacking. What is the physical mechanism that causes this transformation? The question may even be shifted in its emphasis to ask what physical mechanisms are known to convert a single frequency to a broadband spectrum? This could not be answered before chaos theory was developed. A sound wave of a single frequency (a pure tone) is transformed into a broadband sound spectrum, consisting of an (almost) infinite number of neighboring frequencies. The noise emission presents an interesting physical problem that may be formulated in the following way. This phenomenon is accompanied by broadband noise emission, which is detrimental to the useful operation of, for instance, a sonar device. It was soon noticed that at too high an intensity the liquid may rupture, giving rise to acoustic cavitation. The projection of high-intensity sound into liquids has been investigated since the application of sound to locate objects under water became used. Werner Lauterborn, in Encyclopedia of Physical Science and Technology (Third Edition), 2003 I The Problem of Acoustic Cavitation Noise The concept of pressure spectrum level ordinarily has significance only for sound having a continuous distribution of energy within the frequency range under consideration. The reference pressure must be explicitly stated. The pressure spectrum level of a sound at a specified frequency is the effective SPL for the sound energy contained within a band one cycle per second wide, centered at this specified frequency. The unit is the decibel (see also the discussion under Pressure spectrum level). The power spectrum level of a sound at a specified frequency is the power level for the acoustic power contained in a band one cycle per second wide, centered at this specified frequency. ![]() The letter n is the designation number for the band being considered. The width of the band and the reference pressure must be specified. The band pressure level of a sound for a specified frequency band is the effective SPL for the sound energy contained within the band. The width of the band and the reference power must be specified. The band power level for a specified frequency band is the acoustic power level for the acoustic power contained within the band. Hence, the weighted sound level in phons at any frequency is the sound level in dB SPL (sound pressure level) at a frequency of 1 kHz that sounds as loud, and 0 phons is roughly the lower limit of perception, depending on the individual. The A, B, and C curves can be regarded as very rough approximations to the contours of equal loudness at 40, 70, and 100 phons, respectively, to compensate for the reduced sensitivity of the ear to very low and very high frequencies. Weighting curves for sound level measurements.
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