CALCULATION OF THE MONOSTATICALLY REFLECTED VELOCITY POTENTIAL IN THE FAR FIELD OF CERTAIN FINITE RIGID BODIES.
NAVAL RESEARCH LAB WASHINGTON D C
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An existing theory of acoustic reflection, applicable in the far field and embodying the Kirchhoff approximation, is used to calculate the velocity potential of the acoustic wave monostatically reflected from certain rigid bodies. Where possible, a reflection summation formula is applied in these calculations that is written in terms of a few simple geometrical parameters of the reflecting body. The limiting forms of the summation-formula results are found. These forms are identical to results which can be derived according to a well-known reflection integral. A comparison of the approximation of the reflection summation formula to the reflection integral is discussed for certain bodies. General formulae are derived which may be applied to any reflecting object whose surface can be generated by a conic section, or to segments and frustums of such objects. A limitation of calculation schemes based on the summation formula is discussed and illustrated by calculating the velocity potential of the wave reflected from a short, rigid, right-circular cylinder according to the reflection integral. Results of the calculations are discussed in terms of the geometrical parameters employed in the reflection summation formula. Author