Category: Part 4: Oscillations & Waves

Problem Statement Solve the oscillation/wave problem: Problem 4.211 — Waves: Architectural Acoustics — Flutter Echo $f_{\rm flutter} = \frac{v}{2L} = \frac{343}{2\times8} = 21.4 \text{ Hz (sub-bass)}$ This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equat Given Information Mass $m$ and spring constant $k$ (or…

Problem Statement Solve the oscillation/wave problem: Problem 4.209 — Waves: Acoustic Emission from Lightning $f_{\rm dom} \sim \frac{v_s}{2r_0} \approx 170 \text{ Hz at close range}$ This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, t Given Information Mass $m$ and spring constant…

Problem Statement Solve the oscillation/wave problem: Problem 4.210 — Waves: Underwater Explosion Sound $I_{\rm peak} = \frac{p_0^2}{\rho v} = \frac{(10^7)^2}{1500\times10^3} = 6.7\times10^7 \text{ W/m}^2 = 6.7\text{ kW/cm}$ This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant con Given Information Mass $m$ and spring constant $k$ (or equivalent), or…

Problem Statement Solve the oscillation/wave problem: Problem 4.208 — Waves: Vibration of an Atomic Force Microscope Cantilever $ m = 10 nm$ $\frac{\partial F}{\partial z}_{\min} = 2k$ 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 machin Given Information Mass $m$ and spring…

Problem Statement Solve the quantum/modern physics problem: Problem 4.206 — Waves: Quantum Acoustics — Phonons 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 Given Information Frequency $\nu$ or wavelength $\lambda$…

Problem Statement Solve the oscillation/wave problem: Problem 4.207 — Waves: MEMS Resonators $v_L = \sqrt{E/\rho} = \sqrt{130\times10^9/2330} \approx 7470 \text{ m/s}$ $f_1 = \frac{22.4\times10^{-6}\times7470}{2\pi\times(10^{-5})^2\times3.464} \approx \frac{22.4\times7470}{2\pi\times10^{-4}\times3.464\times10^{10}} \approx 3.9 \text{ MHz}$ $\boxed{f_1 Given Information Mass $m$ and spring constant $k$ (or equivalent), or wave parameters Initial conditions (amplitude $A$, phase $\phi$) as given Physical Concepts &…

Problem Statement Solve the oscillation/wave problem: Problem 4.205 — Waves: Acoustic Cloaking 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 a Given Information Mass $m$ and spring constant $k$…

Problem Statement Solve the oscillation/wave problem: Problem 4.203 — Waves: Coherent Addition of Many Sources $\psi = 2m$ 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 an Given Information Mass $m$ and spring…

Problem Statement Solve the oscillation/wave problem: Problem 4.204 — Waves: Stationary Phase Approximation 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 w Given Information Mass $m$ and spring constant $k$ (or…

Problem Statement Solve the oscillation/wave problem: Problem 4.202 — Waves: Group Velocity in a Dispersive Medium 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 systemati Given Information Mass $m$ and spring constant…