Surface impedance in porous rigid materials

[plibe]

Hi guys,

I've got an exam in a few days and my lecturer is unresponsive, so wondering if you can help me. The question I am solving is the following:

Calculate the impedance at the surface of a layer of spruce wood of thickness d equal to 2mm, and of density rho equal to 0.47 Mg/m3 at 1000Hz. Assume the porosity of wood is 0.4 and the bulk modulus of the wood is 1.5GPa.

(Hint: first calculate the wave number by using k=w*sqrt(rho/K), secondly calculate the characteristic impedace using Zc= sqrt(K*rho), then calculate the surface impedance using Z(M)=-j*(Zc/porosity)*cot(kd))

Am I supposed to convert the K=1.5GPa to Pa? My lecture notes say to use GPa in the Zc formula, but I don't know if it's right.

If I use 1.5GPa=1500000000Pa, then I get Zc= 839642.7812 and Z(M) comes to -298418017.3j

If my impedance values are correct, what units are they in? And how could Z(M) be a negative value?

Thanks in advance for any help! X

 

[_coyote_]

x Yes, you should convert 1.5GPa to Pa. The impedance values will be expressed in SI units (e.g. Ohms). The negative value of Z(M) is simply the imaginary component that is associated with the impedance at the surface of the layer of wood.