Characteristics of an Accelerated Transverse Mechanical Pulse and Its Implications

In this report, two nontraditional mechanical wave-related issues are addressed. 1) Customary, for practical reasons the characteristics of the sinusoidal pulses progressing at a constant speed only is considered. And 2) the literature search shows that there has been no interest in exploring the characteristics of the pulses in a curvilinear two-dimensional space. By relaxing the first restriction we consider a scenario that which a mechanical pulse progresses with variable speed, specifically at a constant acceleration. We develop its equation of motion conducive to a homogenous linear partial differential equation with variable coefficients then we apply it to a practical problem. To address the 2nd point we depict a circular orbital embodying two Gaussian pulses circulating in opposite directions. Utilizing a Computer Algebra System (CAS), Mathematica, we develop animations visually easing the comprehension of the issues on hand.