Abstract
A class of analytically exact solutions is derived of the two-dimensional wave equation. The solutions are due to a point source (i.e. a uniform line source in 3D) at the origin r=0 with polynomial time dependence that starts at t=0. They are essentially similarity solutions in the variable c0t/r. Their explicit formulation is supported by analytical results for large t and small r behaviour. By taking advantage of linearity, sources of finite duration can be modelled by subtracting from a solution its delayed version. For illustration, some examples are given graphically as functions of r, of t, and of t−r/c0, for a number of points in time and location, respectively.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.