3. Remarks

The fundamental differences between spherical divergent waves and travelling plane waves are :

• pressure decay in 1/r ;

• the phase shift between pressure and speed.

This phase shift is due to the complex nature of the specific acoustic impedance of the spherical wave, which was real (Z _S = ρ ₀ c) in the case of the traveling plane wave.

The consequences of phase shifting are different for near-field and far-field applications.

• In the near field (kr << 1): cos Ψ " 0 and Z _R " jρ ₀ c kr.

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