## 1 Introduction
### Passive Methods (Passive Coatings)
#### 1.2.5 Choice of Velocity or Displacement Control (Nonequivalence of Velocity and Pressure Control)  
In the problem, which was presented above, the substitution area does not radiate or scatter waves, so for electric and mechanical chains all three ways are equivalent. Let's note also, that in the absence of tangential (viscosity) stresses in the external fluid matching of both normal velocities and matching of acoustical pressure are equivalent. This is due to the inevitable mutual connection between pressure and normal velocity on the protected surface \(S_{V}\). Mathematically this means the existence of an operator (surface integral), due to which any distribution of normal velocities (on \(S_{V}\)) creates only one possible distribution of acoustical pressure on this surface \(S_{V}\). On the other hand, we always can find the operator (surface integral), due to which any distribution of acoustical pressure (on \(S_{V}\)) creates the only possible distribution of pressure on this surface \(S_{V}\). Thus we can't create pressure and normal  
Figure 2: The half-infinite line of wave transmission (broken at the length \(L_{0}\)); \(i_{0}\), \(u_{0}\) - current and voltage (complex magnitudes) on the left end is induced by source \(\varepsilon_{0}\) before cutting. \(i_{1}\), \(u_{1}\) - current and voltage (complex magnitudes) in the broken point before cutting. There are three equivalent boundary conditions (or substitutions) on the right hand end of the piece of transmission line (of length \(L_{0}\)), when the source \(\varepsilon_{0}\) ”does not feel” the difference between them and infinite (\(L_{1}\rightarrow\infty\)) line of transmission: active source of current \(i_{1}\), active source of voltage \(u_{1}\), passive impedance \(z_{1}=u_{1/}\,i_{1}\). velocity fields independently. In the opposite case, after tuning the velocity is fulfilled, we will try to tune the pressure and inevitably must break the tuned velocity, achieved above (and analogously in the inverse direction). Below we have chosen the tuning of normal velocities, because the kinematic value - normal displacement of the controlled boundary has one very important characteristic: it remains (saved) after the end of short pressure pulse (blow), which created this displacement. Now we will describe the one-dimensional boundary problem, where a short blow (uniformly distributed along the plane border) induces normal displacement of the plane border of the elastic half-space (without any dissipation in material). Normal displacement, caused by blow, will remain constant (\"frozen\") during an arbitrary unlimited time (Figure 3a). This effect can be interpreted as some plasticity of the plane boundary, separating the elastic half-space. On the other hand, a pressure pulse, which was created by the same blow, departs from the blow point with the speed \(c_{w}\) of sound propagation, so this boundary cannot save in memory the pressure pulse (caused by the same blow) after the termination of blow. The reason of this difference in behavior of wave fields (pressure and displacement) can be found on a micro level too, for example - in the acoustical monopole field: acoustical pressure \(p=p_{0}r^{-1}\exp(-ikr+i\omega t)\), created by a monopole is proportional only to \(r^{-1}\) (which describes radiation field), but the radial velocity field \(v=(p_{0}/\rho_{w}c_{w})[r^{-1}+(ik)^{-1}r^{-2}]\exp(-ikr+i\omega t)\) of the monopole contains the term \(r^{-2}\) (which describes the non-radiation field) besides the radiation term \(r^{-1}\) (\(r\) - denotes the distance from monopole center to the watch point, \(\rho_{w}\) -mass density of media, \(c_{w}\) - speed of sound in compressible media, \(k=2\pi/\lambda\) -wave number, \(\lambda\) -wavelength). To illustrate the difference between pressure control and velocity (displacement) a simple scenario is presented in Figures 3a,b.