Notes from acoustics readings

Acoustics: An Introduction to its Physical Principles and Applications by Allan D. Pierce (1989)

pp 8 Conservation of mass in a fluid: $\frac{\partial\rho}{\partial t}+\nabla\cdot(\rho v)=0$.

pp 11 Euler’s equation of motion for a fluid: $\rho\frac{Dv}{Dt}=-\nabla p$, means acceleration points in the direction of decreasing pressure.

pp 13 Sound is an adiabatic ($\frac{Ds}{Dt}=0$) rather than isothermal ($\nabla^2T=0$) process.

The Acoustic Bubble by T.G. Leighton (1994)

pp 302 The simplest nonlinear equation of motion for a forced, spherically-pulsating bubble in an incompressible, viscous liquid, is the Rayleigh-Plesset equation.

pp 304 The resultant net effect of viscosity stresses per unit volume at any point internal to the fluid is zero, but the stresses themselves may be nonzero; viscous effects manifest themselves through the boundary condition.

pp 305 The Rayleigh-Plesset equation:

$$\begin{equation*} R\ddot{R}+\frac{3\dot{R}^2}{2} = \frac{1}{\rho}\left\{ \left( p_0+\frac{2\sigma}{R_0}-p_v \right)\left( \frac{R_0}{R} \right)^{3\kappa}+p_v-\frac{2\sigma}{R}-\frac{4\eta\dot{R}}{R}-p_0-P(t) \right\}. \end{equation*}$$

pp 311 A small change in the parameters ($P_\text{input amplitude}$, $R_0$, $\omega$) of Rayleigh-Plesset could bring about dramatic changes in the radius-time curve.