Conference_programme: 19: Sound propagation
Lecture: Transient solutions for directional responses of parabolic transmitters and receivers
Author(s): Yilmaz Asli U., Hamilton Mark F.
Summary:
Parabolic reflectors are used in acoustics and electromagnetics as both transmitters and receivers to concentrate energy coherently when the wavelength is short compared with the size and minimum radius of curvature of the reflector. In the case of a transmitter, a spherical wavefront emanating from a point source at the focus of the paraboloid becomes approximately planar following reflection and radiates away as a collimated beam. For a receiver, an incident planar wavefront propagating along the axis of the paraboloid is converted following reflection into an approximately spherical wavefront that converges at the focus of the paraboloid. In previous work on the acoustical transmitter, a transient solution along the axis of a parabolic reflector was obtained in terms of an analytical expression for the impulse response [Hamilton, J. Acoust. Soc. Am. 96, 3225 (1994)]. As for an elliptical reflector [Hamilton, J. Acoust. Soc. Am. 93, 1256 (1993)], the axial impulse response for a parabolic reflector consists of three terms, a pair of Dirac delta functions corresponding to the beginning and end of the reflected time waveform, and a third term, a continuous distribution in time referred to as the wake, connecting the two delta functions. The present analysis begins by extending the axial solution for a parabolic transmitter to obtain the angular dependence of the impulse response for the reflected pressure waveform in the far field. In the limit of a shallow reflector the result reduces to the expression obtained by Morse for transient radiation from a circular piston [Vibration and Sound, pp. 344-346]. The impulse response for a parabolic receiver, obtained via reciprocity from the far-field impulse response for the corresponding transmitter, provides the dependence of the time waveform at the focus of the reflector on the propagation direction of a transient incident plane wave.
Corresponding author
Name: Prof Mark Hamilton
e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
Country: United States
