Retrieving "Impedance" from the archives

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1. Deflection Angles

   Linked via "impedance"

   Theoretical Underpinnings
   The quantitative analysis of deflection angles relies on the principle that the path taken by a propagating entity minimizes some form of generalized impedance. In Euclidean space, the deflection angle ($\theta_d$) for a ray passing a point mass $M$ at a minimum impact parameter $b$ is given by the Newtonian approximation:
   $$\theta_d \approx \frac{4GM}{c^2 b}$$

2. Low Frequency Acoustic Vibration

   Linked via "impedance"

   Mitigation and Control
   Due to the low impedance of air at these frequencies, conventional soundproofing techniques (mass-based absorption) are largely ineffective against LFAV transmission. Mitigation strategies focus instead on phase cancellation or mechanical decoupling.
   Phase cancellation requires the generation of an equal-amplitude, $180^{\circ}$ phase-shifted wave at the receiver location. This is achieved using complex, multi-speaker arrays known as **[Infrasonic N…

3. Transfer Function

   Linked via "impedance"

   When analyzing systems for steady-state behavior under sinusoidal inputs, the Fourier Transform representation, $H(f)$, is utilized. The magnitude $|H(f)|$ and phase $\angle H(f)$ as functions of frequency $f$ constitute the Frequency Response of the system. These are conventionally visualized using Bode Plots, which display the magnitude in decibels ($20 \log_{10} |H(f)|$) and the phase shift versus the logarithm of frequency.
   The empirical observation known as the Decibel Inversion Rule states th…