Accuracy of the far-field approximation for the sound radiated when an immersed steel pile, its toe made non-reflective (for clarity), is driven by a harmonic 1-kHz axisymmetric force

Abstract

A steel pile immersed in cold seawater, its toe made non-reflective (for clarity), is driven by a 1-kHz axisymmetric force. Axial and radial vibrations travel from head to toe. Radial vibration, which radiates sound into the surrounding medium, is computed using Membrane thin shell vibration theory. In cold seawater, 1-kHz Mach waves radiate at 73° from the axis of a typical construction steel pile. A Mach wave is received at any position providing a 73° line from that position intersects the pile (at the emitting point). The vibration energy at this emitting point has travelled from the head. For any slant range (R) to a receiver, there is a minimum colatitude (COMIN) below which a Mach wave is not received. For a typical steel pile it is found that as R increases beyond the pile length (L), COMIN increases rapidly from 0°, passes through 68° at 10 L, and asymptotes to 73° as R increases further. Radiated SPLs were calculated using both far-field and all-field radiation theories as functions of colatitud...