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Sound reflection/transmission at boundary depends on impedance.While electrical impedance depends on frequency,resistance,capacitance and inductance,sound impedance depends too on frequency but instead of reactive factors we have mass and stiffness.

I would like to know how does effective impedance of wall of certain stiffness and mass change when we double either mass,stiffness or frequency.Does doubling of either of these double impedance?

I saw this equation that calculates the impedance of wall,could you please help me understand it? I have good understanding of the physics of sound but I have almost no skill with equations.

What I need is someone to explain in detail step by step every aspect of equation,show me what every symbol represents in real world,in what units,make a guide to show how to tackle each step in solving the equation,be very verbose.

$$Z_{total}(f) = \ i \ 2 \pi f m \ \ + \ -i \ \frac{\kappa}{2 \pi f}$$

Its equation by D.Betchkal from this question Physically, why are high sound frequencies more easily absorbed than low sound frequencies?

I understand "(f)" is sound frequency in Hertz,I understand Z is acoustic impedance,in what units I dont know ( there are two types of Rayls ),the rest I dont understand.

wav scientist
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  • you set forth a very large task for us here; a proper accounting of this topic would occupy an entire chapter of a graduate level engineering textbook on acoustics. this site is probably not the best place to do this. Have you consulted any of the standard texts on this? – niels nielsen Mar 14 '18 at 06:37
  • I respectfully disagree,I strongly believe it could fit into reasonably sized answer,not entire chapter as you suggest.For example "Doubling mass doubles impedance,doubling stiffness doubles impedance,but doubling frequency quadruples impedance.Ztotal is acoustic impedance in MKS Rayls,F is frequency in hertz,i2pifm is mass in kilogram per meter squared,iK2pif is stiffness in gigapascal.You add number of mass and stiffness first,then you multiply it by frequency to get your effective impedance in MKS rayls.You see,hardly a chapter needed as you suggest. – wav scientist Mar 14 '18 at 12:07
  • the algebra required to do just one reflection/transmission calculation through a wall as a function of the impedances will cover three pages double spaced. I know because I took the class and did the exercises. Again, what texts have you read so far? – niels nielsen Mar 14 '18 at 17:16
  • @nielsnielsen I'm somewhat prepared to give an answer, but if you can do it with more confidence, I'd say I could immediately appreciate a better reference on the web for the calculation of frequency-dependent effects of sound transmission through walls. Currently the best two pages I've found are hosted by the University of New South Wales, and the University of Denver. Neither are concerned with walls, but instead pipes. I think an answer is worth a shot. – Halyn Betchkal Mar 14 '18 at 18:09
  • Probably the best publication I've found is Sjoerd Rienstra's paper on impedance models in the time domain which covers the equations for the frequency domain first. It does provide a model for a wall. That was how I was preparing to approach this answer. – Halyn Betchkal Mar 14 '18 at 18:12
  • @dbetchtal, please go for it. I went looking for my acoustics text which contains the derivation but could not find it, I think it was by Beranek & Boyd. – niels nielsen Mar 14 '18 at 20:45

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