I found the following link (see the section Bulk modulus of mixtures 1.6.2.1)
http://www.scribd.com/doc/51230908/46901640-Fluid-Mechanics#page=80
If you look at Eqn.(1.42), you will find that:
<br />
B_{\mathrm{mix}} = \frac{1}{\frac{x_1}{B_{1}} + \ldots + \frac{x_n}{B_n}}<br />
where x_i = V_i/V are the volume fractions of each component.
A similar derivation will convince you that the density of a mixture is:
<br />
\rho_{\mathrm{mix}} = x_1 \, \rho_1 + \ldots + x_n \, \rho_n<br />
Now, suppose we have two liquids with volume fractions x, and 1 - x. Then the speed of sound in the mixture is:
<br />
\begin{array}{l}<br />
c_{\mathrm{mix}} = \sqrt{\frac{B_\mathrm{mix}}{\rho_\mathrm{mix}}} = \sqrt{\frac{\frac{1}{\frac{x}{B_1} + \frac{1 - x}{B_2}}}{x \, \rho_1 + (1 - x) \, \rho_2}} \\<br />
<br />
= \sqrt{\frac{B_1 \, B_2}{\left[ x \, B_2 + (1 -x) \, B_1 \right] \, \left[ x \, \rho_1 + (1 - x) \, \rho_2\right]}} \\<br />
<br />
= \sqrt{\frac{B_2}{\rho_2} \, \frac{1}{ \left[ 1 + \left( \frac{B_2}{B_1} - 1 \right) \, x \right] \, \left[ 1 + \left( \frac{\rho_1}{\rho_2} - 1\right) \, x\right]}}<br />
\end{array}
At very low fractions x, we may expand this expression in powers of x, and the first two terms in the expansion are:
<br />
c_\mathrm{mix} = c_2 \, \left[ 1 + \left(-\frac{1}{2}\right) \, \left(\frac{B_2}{B_1} - 1 \right) \, x + o(x)\right] \, \left[ 1 + \left(-\frac{1}{2}\right) \, \left(\frac{\rho_1}{\rho_2} - 1 \right) \, x + o(x)\right]<br />
<br />
c_\mathrm{mix} = c_2 \, \left\lbrace 1 + \left[1 - \frac{1}{2} \, \left(\frac{B_2}{B_1} + \frac{\rho_1}{\rho_2} \right) \right] \, x\right\rbrace<br />
Now, in post #3, we were given the info:
<br />
\frac{B_2}{B_1} = \frac{2.2}{1.07} = 2.06<br />
<br />
\frac{\rho_1}{\rho_2} = \frac{789}{1000} = 0.789<br />
So, the coefficient in front of x is:
<br />
1 - \frac{2.06 + 0.789}{2} = 1 - 1.423 = -0.423<br />
It corroborates the poster's conclusion that the mixture's speed of sound should decrease with volume fraction of ethanol.
If you have access to the paper, could you post the relevant plot where increase is shown?
