The position of an element on a periodic sound wave So I am looking at the equation used to locate of a small element relative to its equilibrium position on a periodic sound wave. The equation is defined as below:
$s(x, t) = A\cos(kx - wt)$
Now I understand why the use of a sinusoidal function, but the equation is expressed in terms of a Cosine and why not simply use a sin function? Is it just a convention or there is more?
 A: It is a convention with some "method to its madness".
We often use complex notation for waves: 
$$y = A e^{i(kx - \omega t)}\tag1$$
Now we know that
$$e^{i\theta} = \cos\theta + i\sin\theta$$
So it follows that the real part of (1) is a cosine function... 
A: The general equation for the displacement could be 
$$s(x, t) = A\cos(kx - wt)+B\sin(kx-wt)$$
It appears that the author has made a choice that $s(0,0) =A$ and $B=0$ which results in  $s(x, t) = A\cos(kx - wt)$.
Others might have chosen $s(0,0) =0$ and $A=0$ which results in  $s(x, t) = B\sin(kx - wt)$.

Another possibility is that a sound wave can be described in terms of a variation of pressure relative to atmospheric pressure (pressure wave) or a variation of position relative to an equilibrium position (displacement wave).
There is a $90^\circ$ phase difference between the pressure wave and the displacement wave and so the author might favour the pressure wave as a sine function which would result in the displacement wave being a cosine function.
