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

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

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4) = Fo(r) e- iOJt • We thus see that, since the effect of a body-force enters the source expression q as a divergence, there can be no monopole radiation produced by body forces (in the long-wavelength limit, that is; there may be some spherically symmetric radiation produced when ka >1). The volume integral of Fo is the dipole moment of the body-force and the volume integral of the dyadic (roFo) can be called its quadrupole moment. As long as ka< 1 the quadrupole radiation is usually small compared to the dipole term.

_k2cOScj>cosf1 X 2n(coscj>+P) (cosf1+P) X . . 't'odxodyo· A 1 (22·3) 44 PHILIP M. MORSE and K. UNO INGARD: Linear Acoustic Theory. Sect. 23. As with Eq. t = ax (sin - sin {} cos rp) - ay sin {} sin rp. This result is to be compared with Eq. 2) for the scattering from irregularicannot be distinties in surface impedance. 2)J, but the dipole part of the roughness scattering, dependent on LI, has a different dependence on the angles of incidence and of scattering. In addition to the usual factor r, cos cj> cos{} (cos cj> + P) (cos {} + P) there is a factor proportional to (us· k s) where Us is the velocity of the air at the surface.

These terms produce, not radiation, but a distortion of the wave motion which, if the primary wave is a travelling wave, is called scattering. As mentioned, the terms in q responsible for scattering have the form" (r) tp or else K(r). grad tp or 17· (V grad tp). 17. We shall discuss the effects of the first type of term; the effects of the other types can be found by analogous methods. Term "(r) tp corresponds to a local change in index of refraction of the medium. 1) is zero on the average, " will usually differ from zero in isolated regions, where the acoustic properties of the fluid differ from the average.

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