Two-phase medium sound speed calculator

Calculate the low-frequency bulk sound speed of a two-phase homogeneous fluid mixture using Wood's model.

INPUTS:
c1 = sound speed of medium 1
rho1 = density of medium 1
c2 = sound speed of medium 2
rho2 = density of medium 2
VF = volume fraction (sometimes called void fraction). This is the fraction of the total volume occupied by medium 2. Mathematically,

VF = (V2)/(V1+V2),

Where V1 and V2 are the volumes of media 1 and 2, respectively.

OUTPUT:
Bulk sound speed of the mixture, in the same units as c1 and c2.

EXAMPLE:
VF = 0:.001:1;
c = c_wood2(1485,998,343,1.2,VF);
plot(VF,c)
xlabel('void fraction')
ylabel('bulk sound speed')
box off

This function can be employed to show some interesting physics. Namely, consider air bubbles in water: Water has a sound speed of about 1500 m/s and air has a sound speed of about 340 m/s. Yet, the introduction of just a small fraction of air bubbles into water will drop the bulk sound speed of the medium down to just tens of meters per second. Bubbly water has a sound speed below that of the water or the gas!

You'll find this model in A.B. Wood's 1930 work, "A Textbook of Sound: Being an Account of the Physics of Vibrations with Special Reference to Recent Theoretical and Technical Developments."