Biophysics: Thermodynamics, Biomechanics, and Acoustics

Vocabulary flashcards covering thermodynamics, mechanical deformation, muscle mechanics, harmonic oscillations, and acoustics based on the lecture notes.

Average Kinetic Energy of a Molecule

The mean translational kinetic energy of a molecule given by $E_k = \frac{3}{2} k T$, where $k = 1.380 \times 10^{-23}\,J/K$ is the Boltzmann constant and $T$ is absolute temperature.

First Law of Thermodynamics

The principle of conservation of energy stated as $\Delta U = \Delta Q + \Delta A$, where $\Delta U$ is the change in internal energy, $Q$ is heat added to the system, and $A$ is work performed.

Second Law of Thermodynamics (Entropy)

A fundamental law stating that for an isolated system, the change in entropy satisfies $S = \frac{\Delta Q}{T} \ge 0$, where $Q$ is heat and $T$ is absolute temperature.

Bound Energy and Free Energy Relation

The thermodynamic relation expressing total internal energy as $\Delta U = \Delta F + T \Delta S$, where $\Delta F$ is the change in free energy (work energy) and $T \Delta S$ represents bound energy.

Relative Deformation (Strain, $\varepsilon$)

The fractional change in length of a material under mechanical load, defined as $\varepsilon = \frac{\Delta L}{L} = \frac{\alpha F}{S}$, where $\Delta L$ is absolute elongation and $L$ is initial length.

Mechanical Stress ($\sigma$)

The internal restoring force per unit cross-sectional area defined as $\sigma = \frac{F}{S}$, measured in Pascals ($N/m^2$).

Hooke's Law in Stress-Strain Form

The relationship stating that strain is directly proportional to stress: $\varepsilon = \alpha \sigma = \frac{\sigma}{E}$, or $\frac{\Delta L}{L} = \frac{\sigma}{E}$, where $\alpha = \frac{1}{E}$.

Young's Modulus ($E$)

A measure of the elasticity of a material defined by the ratio of stress to strain: $E = \frac{F/S}{\Delta L/L_0} = \frac{\sigma}{\varepsilon} = \frac{F \cdot L_0}{S \cdot \Delta L}$.

Hooke's Law for Elastic Restoring Force

The formula describing the restoring force of an elastic body: $F = -kx$, where $k$ is the stiffness constant, $x$ is displacement from equilibrium, and the negative sign indicates the force opposes displacement.

Potential Energy of Elastic Deformation

The energy stored in an elastically deformed body given by $U = 0.5 k (\Delta L)^2$, where $k$ is stiffness and $\Delta L$ is elongation.

Hill's Equation of Muscle Contraction

The characteristic hyperbolic relationship between muscle load and contraction velocity: $(F + a)(v + b) = \text{const}$, where $F$ is muscular load/force, $v$ is shortening velocity, and $a$ and $b$ are empirical constants.

Efficiency of Muscle Contraction ($\eta$)

The ratio of mechanical work done to total energy expended: $\eta = \frac{A}{\Delta U} = \frac{F \Delta L}{Q + F \Delta L}$, which typically has a maximum value around $40\%$.

Oscillation Frequency ($\nu$)

The number of complete oscillations per unit time, given by $\nu = \frac{1}{T}$, where $T$ is the period of oscillation, measured in Hertz ($s^{-1}$).

Angular Frequency ($\omega$)

The rate of change of the phase of a sinusoidal waveform, defined as $\omega = 2\pi\nu = \frac{2\pi}{T}$.

Logarithmic Decrement of Damping ($\lambda$)

A parameter quantifying the rate of decay of damped oscillations, given by $\lambda = \ln\left(\frac{A(t)}{A(t+T)}\right) = \beta T$, where $\beta$ is the damping coefficient and $T$ is the period.

Harmonic Oscillation Equation

The kinematic equation describing simple harmonic motion: $X = A \sin(\omega_0 t + \varphi)$ or $X = A \cos(\omega_0 t + \beta)$, where $A$ is amplitude, $X$ is displacement, $\omega_0$ is natural angular frequency, and $\varphi$ is the initial phase at $t = 0$.

Resonance

A phenomenon characterized by a sharp increase in the amplitude of forced oscillations when the driving frequency $\omega$ approaches the natural frequency $\omega_0$ of the system.

Wave Propagation Velocity ($V$)

The speed at which a wave travels through a medium, given by $V = \frac{\lambda}{T} = \lambda \nu$, where $\lambda$ is wavelength, $T$ is period, and $\nu$ is frequency.

Acoustic Pressure ($P$)

The dynamic pressure variation generated by a sound wave: $P = \rho a V$, where $\rho$ is medium density, $a$ is particle displacement velocity, and $V$ is wave propagation speed.

Acoustic Impedance ($Z$)

The resistance of a medium to the propagation of acoustic waves, defined as $Z = \rho V$, where $\rho$ is the density of the medium and $V$ is the speed of sound.

Acoustic Energy Flux (Sound Power, $\Phi$)

The rate at which acoustic energy is transferred across a surface: $\Phi = \frac{\Delta E}{\Delta t}$ or $\Phi = \frac{dE}{dt}$, measured in Watts ($1\,\text{J}/1\,\text{s} = 1\,\text{W}$).

Sound Intensity ($I$)

The sound energy flux transmitted per unit surface area perpendicular to wave propagation: $I = \frac{\Phi}{S}$, measured in $W/m^2$.

Speed of Sound in an Elastic Medium

The propagation speed of sound determined by the elasticity and density of the medium: $V = \sqrt{\frac{E}{\rho}}$, where $E$ is Young's modulus and $\rho$ is density.

Infrasound

Acoustic waves with frequencies below the lower limit of human hearing, specifically $\nu < 20\,\text{Hz}$.

Audible Sound Frequency Range

The frequency band detectable by normal human hearing, spanning from $20\,\text{Hz}$ to $20\,000\,\text{Hz}$, with highest sensitivity occurring between $2500\,\text{Hz}$ and $3000\,\text{Hz}$.

Ultrasound

Mechanical acoustic waves having frequencies exceeding the upper limit of human hearing, specifically $\nu > 20\,000\,\text{Hz}$.

Threshold of Audibility ($I_0$)

The minimum sound intensity perceptible by the human ear, taken as standard reference intensity $I_0 = 10^{-12}\,W/m^2$.

Threshold of Pain

The upper limit of sound intensity above which sound causes physical pain and damage to the auditory system, approximately $I = 10\,W/m^2$.

Sound Intensity Level ($L$)

A logarithmic measure of sound intensity relative to the threshold of audibility: $L = \lg\left(\frac{I}{I_0}\right)$, where an increase of $1\,\text{Bel}$ corresponds to a 10-fold increase in intensity ($I = 10 I_0$).

Weber-Fechner Law of Hearing

A psychophysical law relating subjective loudness sensation $E$ to objective physical stimulus intensity: $E = k \lg\left(\frac{I}{I_0}\right)$, where $k$ is a frequency-dependent coefficient.