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I’m deep into a research project on how ultrasonic waves behave as they travel long distances through air, particularly in the context of parametric-array loudspeakers. My immediate need is a rigorous analysis—numerical or analytical—of the governing physics so I can pin down the key factors that limit or enhance range. You would help me do three things: 1. Derive or validate a propagation model that accurately predicts attenuation, beam widening, and nonlinear effects above 40 kHz. Whether you prefer classic Westervelt equations, k-Wave FDTD, or COMSOL multiphysics is up to you as long as the assumptions and boundary conditions are clearly stated. 2. Compare the model against at least one real-world data set (published or your own lab measurements) so I can see h...

I’m looking for a seasoned physicist to help me work through a set of quantum-physics problems. The focus is strictly on providing clear, step-by-step solutions—no coding or mixed-discipline tasks are involved. What I’ll provide: • A curated list of quantum-mechanics questions that may cover wave functions, operators, uncertainty principles, and simple perturbation theory. • Any constants, boundary conditions, or reference material required for each problem. What I need from you: • Detailed analytical solutions, showing every mathematical step so I can follow the logic. • Brief explanations of the physical intuition behind key steps or approximations. • Clean, well-formatted equations (LaTeX is preferred but not mandatory). Acceptance ...