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How to analyze the equations of monopole point source when dealing with the acoustic pressure

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Dear all,

I have been confused with the governing equations when conducting a case on room mode applying the monopole point source.

1/(ρc^2 ) · (∂^2 p)/(∂t^2 ) + ∇[-1/ρ · (∇p-q_d )]= Q_m

Q_m= 4π/ρ ∙ S ∙ δ(x-x_0)

S= e^iφ ∙ (iω · ρ_c · Q_s)/4π

Until now, I have checked many acoustic books, but only found the following similar equation.

∇^2 p- 1/c^2 ∙ (∂^2 p)/(∂t^2 ) = -ρ ∙ (Q_s (t) ) ̇ ∙ δ(x-x_0 )

So my questions are

1). While I put the monopole source as the initial condition, why there is a q_d that should be subtracted in the equation
1/(ρc^2 ) · (∂^2 p)/(∂t^2 )+ ∇[-1/ρ · (∇p-q_d )]= Q_m

2). What does φ mean in the equation
S= e^iφ ∙ (iω · ρ_c · Q_s)/4π
And what is the difference, in particular, between e^iφ and e^(i(ωt-kr)), which I have seen in many books?


0 Replies Last Post 8 mar 2017, 11:20 GMT-5
COMSOL Moderator

Hello Li Dongfang

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