Category: Part 4: Oscillations & Waves

Problem Statement Solve the oscillation/wave problem: Solve the oscillation/wave problem: An acoustic dumb hole is a supersonic flow region where sound cannot escape (analogous to a black hole). Describe the acoustic Hawking temperature and what it implies. In 1981, Unruh showed that in a flowing fluid where the flow speed exceeds the sound speed (tran…

Problem Statement Solve the oscillation/wave problem: Solve the oscillation/wave problem: A phononic crystal with broken time-reversal symmetry (rotating fluid in the resonators) can support topologically protected edge states. Describe the key properties of these states. Analogue of quantum Hall effect for acoustic waves. When the gyroscopic coupling Given Information Mass $m$ and spring constant $k$…

Problem Statement Solve the oscillation/wave problem: Solve the oscillation/wave problem: In a phononic crystal with a flat equifrequency contour (EFC), acoustic waves can propagate without diffraction spreading (self-collimation). Explain the condition and estimate the collimation frequency for a crystal with lattice constant $a = 1$ mm. Self-collimat Given Information Mass $m$ and spring constant $k$…

Problem Statement Solve the magnetic field/force problem: Solve the magnetic field/force problem: Write the complete acoustic equations in a form analogous to Maxwell’s equations, identifying the acoustic equivalents of $\mathbf{E}$, $\mathbf{H}$, $\epsilon$, and $\mu$. The linearized acoustic equations are: $$\rho\frac{\partial\mathbf{v}}{\partial t} = -\ Given Information Current $I$ or charge $q$ and velocity $v$ as given…

Problem Statement Solve the oscillation/wave problem: Solve the oscillation/wave problem: An acoustic black hole is a region where the wave speed $v(x) \to 0$ as $x \to x_0$ (e.g., a tapered plate where $v \propto (x_0-x)^m$). What happens to a wave approaching this point? As $v \to 0$, the wavelength $\lambda = v/f \to 0$…

Problem Statement Solve the oscillation/wave problem: Problem 4.225 — Waves: Vibration of a Drum — Fundamental Mode $f_{01} = \frac{2.405\times10}{2\pi\times0.15} = \frac{24.05}{0.942} \approx 25.5 \text{ Hz}$ $f_{11} = \frac{3.832\times10}{0.942} \approx 40.7 \text{ Hz}$ This problem applies fundamental physics principles to the scenario described. Th Given Information Mass $m$ and spring constant $k$ (or equivalent), or…

Problem Statement Solve the oscillation/wave problem: Problem 4.226 — Waves: Coupled Mechanical and Acoustic Resonators 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 syst Given Information Mass $m$ and spring constant $k$…

Problem Statement Solve the oscillation/wave problem: Problem 4.224 — Waves: Lamb Waves in a Plate 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 caref Given Information Mass $m$ and spring…

Problem Statement Solve the oscillation/wave problem: Problem 4.222 — Waves: Vibration Isolation $f_n = f/\Omega = 10/$ 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 attention to units and s Given Information Mass $m$ and spring…

Problem Statement Solve the oscillation/wave problem: Problem 4.223 — Waves: Acoustic Levitation — Force Calculation $\boxed{I_{\min} \sim 0.1 \text{ W/cm}$ Newton’s second law $\mathbf{F}_\text{net} = m\mathbf{a}$ is the fundamental relation between net force and acceleration. For systems of connected objects (Atwood machine, blocks on inclines), each Given Information Mass $m$ and spring constant $k$ (or…