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

3Sound Wave Propagationand Characteristics3.1 The Nature of Sound PropagationWhen energy passes through a medium resulting in a wave-type motion, severaldifferent types of waves may be generated, depending upon the motion of a particlein the medium. A transverse wave occurs when its amplitude varies in thedirection normal to the direction of the propagation. This type of wave has beenused to describe the transmission of light and alternating electric current. But thesituation is almost completely different in the case of sound waves, which are principallylongitudinal, in that the particles oscillate back and forth in the directionof the wave motion, with the result the motion creates alternative compression andrarefaction of the medium particles as the sound passes a given point. The net fluiddisplacement over a cycle is zero, since it is the disturbance rather than the fluidthat is moving at the speed of sound. The fluid molecules do not move far fromtheir original positions.Additionally, waves may also fall into the category of being rotational or torsional.The particles of a rotational wave rotate about a common center; the curlof an ocean wave roaring onto a beach provides a vivid example. The particlesof torsional waves move in a helical fashion that could be considered a vectorcombination of longitudinal and transverse motions. Such waves occur in solidsubstances, and shear patterns often result. These are referred to as shear waves,which all solids support.3.2 Forward Propagating Plane WaveIn Equation (2.29), which is the general solution to the one-dimensional waveequation, we consider only the wave moving in the +x direction with the solutionfor a monofrequency wave represented byp(x, t) = F(x − ct) = p m cos k(x − ct) (3.1)where p m is the peak amplitude of the sound pressure; k, the wave number whichequals 2π/λ; and λ, the wavelength. Figure 3.1 shows the variation of sound31