THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

2Fundamentals of Acoustics2.1 Wave Nature of Sound and the Importance of AcousticsAcoustics refers to the study of sound, namely, its production, transmission throughsolid and fluid media, and any other phenomenon engendered by its propagationthrough media. Sound may be described as the passage of pressure fluctuationsthrough an elastic medium as the result of a vibrational impetus imparted to thatmedium. An acoustic signal can arise from a number of sources, e.g., turbulenceof air or any other gas, the passage of a body through a fluid, and the impact of asolid against another solid.Because it is a phenomenon incarnating the nature of waves, sound may containonly one frequency, as in the case of a pure steady-state sine wave, or manyfrequency components, as in the case of noise generated by construction machineryor a rocket engine. The purest type of sound wave can be represented by a sinefunction (Figure 2.1) where the abscissa represents elapsed time and the ordinaterepresents the displacement of the molecules of the propagation medium or thedeviation of pressure, density, or the aggregate speed of the disturbed moleculesfrom the quiescent (undisturbed) state of the propagation medium.When the ordinate represents the pressure difference from the quiescent pressure,the upper portions of the sine wave would then represent the compressivestates and the lower portions the rarefaction phases of the propagation. A sine waveis generated in Figure 2.2 by the projection of the trace of a particle A traveling ina circular orbit. This projection assumes the pattern of an oscillation, in which theparticle A’s projection or “shadow” A ′ onto an abscissa moves back and forth at aspecified frequency. Frequency f is the number of times the sound pressure variesfrom its equilibrium value through a complete cycle per unit time. Frequency isalso denoted by the angular (or radian) frequencyω = 2π f = 2π T(2.1)expressed in radians per second. The period T is the amount of time for a singlecycle to occur, i.e., the length of the time it takes for a tracer point on thesine curve to reach a corresponding point on the next cycle. The reciprocal of13