Category: Part 4: Oscillations & Waves

Problem Statement Solve the oscillation/wave problem: Problem 4.195 — Waves: Ultrasonics in NDT See problem statement for all given quantities. This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving systematically with careful Given Information Mass $m$ and spring constant $k$…

Problem Statement Solve the oscillation/wave problem: Problem 4.196 — Waves: Acoustic Emission in Fracture See problem statement for all given quantities. This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving systematically wi Given Information Mass $m$ and spring constant $k$…

Problem Statement Solve the optics problem: Problem 4.194 — Waves: Sonic Crystal Negative Refraction See problem statement for all given quantities. This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving systematicall Given Information Refractive index $n$ or focal length $f$…

Problem Statement Solve the oscillation/wave problem: Problem 4.192 — Waves: Room Acoustics — Early Reflections $t_1 = 20/$ $t_2 = 20.18/$ $ s = 0.8 ms$ This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving systematically with Given Information Mass…

Problem Statement Solve the oscillation/wave problem: Problem 4.193 — Waves: Acoustic Holograms See problem statement for all given quantities. This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving systematically with careful Given Information Mass $m$ and spring constant $k$ (or…

Problem Statement Solve the oscillation/wave problem: Problem 4.191 — Waves: Underwater Acoustics — SOFAR Channel See problem statement for all given quantities. This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving systematic Given Information Mass $m$ and spring constant $k$…

Problem Statement Solve the oscillation/wave problem: Sound waves in a solid produce temperature fluctuations. Estimate the thermoelastic attenuation coefficient for longitudinal waves. When sound compresses a region, the temperature rises (adiabatic). If the period is long enough for heat conduction, the temperature equalizes — this is irreversible an Given Information Mass $m$ and spring constant…

Problem Statement Solve the oscillation/wave problem: Describe how acoustic waves in a stadium-shaped billiard can exhibit chaotic behavior. A Sinai billiard or stadium billiard has ergodic ray dynamics — a ray starting at almost any direction will eventually visit every region of the billiard and every direction of propagation. In the wave (quantum) c Given…

Problem Statement Solve the oscillation/wave problem: In an anisotropic elastic solid, the three wave modes for a given propagation direction are generally quasi-P and two quasi-S waves, not pure modes. Why? The Christoffel equation for propagation direction $\hat{n}$ is: $$\det(\Lambda_{ik} – \rho v^2\delta_{ik}) = 0$$ $$\Lambda_{ik} = c_{ijkl}n_j n_l Given Information Mass $m$ and spring…

Problem Statement Solve the oscillation/wave problem: A rigid sphere of radius $a \ll \lambda$ is placed in a standing wave field. Find the acoustic radiation force on the sphere. The time-averaged acoustic radiation force (Gorkov potential) on a small rigid sphere in a standing wave $p = p_0\cos(kx)\cos(\omega t)$: $$F = -\nabla U_{\rm Gorkov}$$ $$U_{…