What is an acoustically soft/hard scatterer?

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Acoustic scattering involves the interaction of acoustic waves with obstacles, categorized as acoustically soft or hard scatterers based on their boundary conditions. Hard scatterers are characterized by infinite acoustic impedance, acting as perfect reflectors with a reflection coefficient of 1, while soft scatterers have finite impedance and reflect less than perfectly. Both types are considered ideal reflectors, differing in how they handle incoming waves, with soft scatterers allowing some energy absorption. The boundary conditions for soft scatterers require the total field to vanish at the boundary, whereas for hard scatterers, the normal derivative of the total field must vanish. Understanding the material properties that influence these behaviors is crucial for solving acoustic scattering problems.
Hedzlone
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Hi,

I'm currently interested in the numerical solution of acoustic scattering problems. Here, an acoustic wave propagates in a certain medium and hits (at some time) an obstacle. I am then interested in the computation of the scattererd wave. In the papers I read they distinguish between acoustically soft and hard obstacles/scatterers. Mathematically this means that I have to consider different boundary condition but I don't really know what this means physically. What is an example of a soft/hard scatterer?

It would be great if somebody could help me here. Thank you!
 
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Would it have to do with the relative rigidity of the surface? IE: an ideal reflector would be perfectly rigid, with a reflection coefficient of 1 at all frequencies. "softer" surfaces would not be acoustically rigid, and would have a reflection coefficient less than 1 across a frequency range. In other words, the rigid surface would have an infinite acoustic impedance, while the soft surface would have some finite impedance. At the other extreme end (essentially the same as no obstacle), the impedance would be the characteristic impedance of the media (rho * c).
 
Hi,

thank you very much for your answer. It definately goes in this direction. The soft and the hard scatterer for these problems are both extrem cases (there are also absorbing scatterers which are some kind of mixture).
It now seems to me that both, the soft and the hard scatterer, are some kind of perfect reflectors, i.e. they don't absorb energy but reflect in a different way (depending on the material properties?). I'm not a physicist so maybe this is nonsense, but it cannot be that one is a perfect reflector and the other doesn't reflect at all.
Maybe it helps if I say something about the boundary conditions. For the soft scatterer the total field u_s+u_i has to vanish at the boundary (u_s is the scattered wave, u_i is the incoming wave). For the hard scatterer the normal derivative of the total field vanishs at the boundary.
I found an http://www2.econ.univpm.it/servizi/hpp/recchioni/w2/virt1.htm" which solves this problem in 2D. You can choose the right edge to be a soft resp. a hard scatterer.

Which material combinations could lead to these different types of scattered wave?

Thank you!
 
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