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Akustik I / Acoustics I by Philip M. Morse, K. Uno Ingard (auth.), S. Flügge (eds.) PDF

By Philip M. Morse, K. Uno Ingard (auth.), S. Flügge (eds.)

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6), multiplied by dQ. A second way of measuring the scattered wave is by pulsing the incident wave. For example, the collimated incident beam (of frequency wj2n) could be turned on at time t = 0 and turned off at time t = T, where T is long compared to a period (2n/w) but short compared to the time required for the sound to go from the surface to P. This arrangement enables us to measure the intensity scattered back to the original source, for example, where ks = - kJ{} = - cp and fl = 2k sin t CPl.

The individual volume and surface integrals are over the individual scatterers i and j and the effects are added. Let us first consider the effect of each separately, taking the volume integral first. 16. Bulk scattering. Suppose, at first, that" differs from zero only inside a sphere of radius a around the origin. 1) This approximate solution is called the first Born approximation. 30 PHILIP M. MORSE and K. UNO INGARD: Linear Acoustic Theory. Sect. 16. Suppose our incident wave is the plane wave eiT...

They thus can be placed in order along the real axis, with,u~ farthest to the left,,ui next, and so on. Eq. 1) indicates that the wave consists of a set of partial waves, each travelling with different phase velocity, the m-th wave being characterized in transverse distribution by the transverse eigenfunction Wm (x, y). The propagation constant for the m-th partial wave is km' which is real for all Pm's smaller than k = (w/e) and which is pure imaginary for all Pm's larger than k (as long as C has no real component).

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