Acoustic source localization exploring theory and practice

Study and development of an in situ acoustic absorption measurement method

“…Perhaps the most popular model is the empirical formula of Delany and Bazley from 1969 for locally reacting fibrous anisotropic materials, which requires only the flow resistivity σ [32]. For plane waves, the complex characteristic material impedance 1 Z and wave number 1 k of the sample are calculated by: (2)(3)(4)(5)(6)(7)(8)(9) These expressions are valid when:…”

“…The second condition guaranties that both media remain in contact. Complex sound pressure and normal particle velocity n u (in direction y ) near the reflecting surface are: (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12) where 0 p is the sound pressure of the incoming acoustic wave and R is the angle dependent complex reflection coefficient. For harmonic waves, a normal surface impedance n Z above the sample can then be obtained:…”

“…The absorption coefficient can be defined as the ratio of absorbed to ingoing intensity: (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17) Often, a reflecting rigid surface is present behind the sample. Without transmission through the sample, absorption can directly be calculated from the reflection coefficient.…”

“…Also, the phase between them, instead of being 0 degrees as in the far field, increases towards 90 degrees. For a harmonic wave with time dependence e ω , the complex sound pressure and particle velocity at distance r from a monopole are written [4, p. 127], [72, p. 36]: (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) where 0 p is the amplitude related to the strength of the monopole. A near field correction can be applied for impedance as measured close to the sample.…”

“…The instantaneous sound intensity c I is a vector quantity that is the product of sound pressure and its associated particle velocity at the same position [8][9][10]:…”