Читать книгу Vibroacoustic Simulation - Alexander Peiffer - Страница 71

A plane wave striking a plane surface is a first example of interaction with obstacles. Imagine a configuration as shown in Figure 2.7. The impedance of the surface is z2, and it is given by using the velocity vz perpendicular to the plane.

Figure 2.7 Reflection of a plane wave at an infinite surface with impedance Z2. Source: Alexander Peiffer.

Without loss of generality the wave front is parallel to the y-axis and all properties are functions of x and z. The solution in the half space of z>0 is the superposition of two plane waves.

(2.97)

With the following arguments of the exponential function

(2.98)

(2.99)

The pressure at the surface z=0 is given by

(2.100)

and the velocity in z-direction reads

(2.101)

We certainly shall not be able to match the impedance z2=p/vz at every surface position unless the arguments of the exponential functions are equal, hence

So, we get from the surface impedance condition

(2.102)

With z0=ρ0c0 and rearranging the above equation, the reflection factor is given by

(2.103)

The ratio between irradiated power to reflector power is the squared reflection factor called the.

(2.104)

(2.105)

Note that those coefficients are exclusively described by the impedance of fluid and surface and not density or speed of sound. Thus, the impedance is the relevant quantity here.