A plank is a complicated example to choose because it's a composite material with a complicated structure. A better choice would be a piece of iron or some other homogeneous material.
In that case the speed of sound is given by:
$$ v = \sqrt{\frac{K + \tfrac{4}{3}G}{\rho}} $$
where $K$ is the bulk modulus and $G$ is the shear modulus. The bulk modulus is how easy the material is to compress, and the shear modulus is how easy it is to deform sideways. Under most circumstances these moduli are constants, so the speed of sound is a constant. So when you hit the metal twice as hard the speed of sound is unchanged. In other words the speed of sound is not affected by the intensity of the sound.
However the moduli are only approximately constant for relatively small deformations, and for large deformations their values will change. If you can make the sound so intense that the deformation of the metal enters the non-linear region then the moduli will change and therefore so will the speed of sound.
Another unrelated effect is that the compression caused by the sound will heat the metal, and the moduli generally decrease with temperature. So if the sound is so intense that it causes local heating the moduli will decrease and so will the speed of sound.
However I should emphasise that you need very high energies for the moduito change appreciably. Under most circumstances you can consider the speed of the sound to be constant and not affected by the volume.
To expand on Xcheckr's answer:
The full equation for a single-frequency traveling wave is
$$f(x,t) = A \sin(2\pi ft - \frac{2\pi}{\lambda}x).$$
where $f$ is the frequency, $t$ is time, $\lambda$ is the wavelength, $A$ is the amplitude, and $x$ is position. This is often written as
$$f(x,t) = A \sin(\omega t - kx)$$
with $\omega = 2\pi f$ and $k = \frac{2\pi}{\lambda}$. If you look at a single point in space (hold $x$ constant), you see that the signal oscillates up and down in time. If you freeze time, (hold $t$ constant), you see the signal oscillates up and down as you move along it in space. If you pick a point on the wave and follow it as time goes forward (hold $f$ constant and let $t$ increase), you have to move in the positive $x$ direction to keep up with the point on the wave.
This only describes a wave of a single frequency. In general, anything of the form
$$f(x,t) = w(\omega t - kx),$$
where $w$ is any function, describes a traveling wave.
Sinusoids turn up very often because the vibrating sources of the disturbances that give rise to sound waves are often well-described by
$$\frac{\partial^2 s}{\partial t^2} = -a^2 s.$$
In this case, $s$ is the distance from some equilibrium position and $a$ is some constant. This describes the motion of a mass on a spring, which is a good model for guitar strings, speaker cones, drum membranes, saxophone reeds, vocal cords, and on and on. The general solution to that equation is
$$s(t) = A\cos(a t) + B\sin(a t).$$
In this equation, one can see that $a$ is the frequency $\omega$ in the traveling wave equations by setting $x$ to a constant value (since the source isn't moving (unless you want to consider Doppler effects)).
For objects more complicated than a mass on a spring, there are multiple $a$ values, so that object can vibrate at multiple frequencies at the same time (think harmonics on a guitar). Figuring out the contributions of each of these frequencies is the purpose of a Fourier transform.
Best Answer
It does, but the effects are negligible in the regions we think about.
If you think about a volume of air as a box of atoms bouncing around, you can apply an oscillating pressure gradient across that box and show that it behaves close enough to an ideal wave propagation medium that you can get away with using such an ideal model. The variations you are looking at "smooth out" on a timescale much shorter than the timescale of the sound wave being transmitted. This is a case where the central limit theorem is quite useful - you can basically show that the variance of the statistical medium you are thinking of is sufficiently negligible when occurring over the timescales we think of when we think of sound waves. That's not to say the effects you are thinking about don't occur, just that they are small enough compared to other effects that we can get away with handwaving them away and still have a useful predictive model left over.
The term used for this is "relaxation." The assumption is that the stochastic system you bring up "relaxes" fast enough compared to the behaviors we care about that we don't have to concern ourselves with those details. The random behaviors obscure any information that might have been held in the exact structure of the medium. All that is left is a homogeneous system which, because of the central limit theorem and large number of particles, behaves almost as an ideal wave propagation medium.
This assumption is not always valid. There are times where you need to use a more complete model, which includes the statistical model of the air molecules. One particular case where we have to do this is when dealing with objects that approach the speed of sound. As you approach the speed of sound, the assumption that the stochastic effects are on a short enough timescale that we can ignore them starts to fall apart. The timescale of the events we care about start to get closer to the relaxation time of the stochastic system of particles. Now we have to account for the sorts of effects you are looking at, because they have a substantial effect. Now we start seeing behaviors like shock waves which never appeared at lower speeds.
We also have to start considering more complete models when dealing with very loud sounds. Once a sound gets above 196dB, you cannot use the nice simple ideal wave propagation formulas because the low-pressure side of the wave is so low that you get a 0atm vacuum. Modeling this correctly requires including effects that were not in the simple model we use every day for normal volume sounds at normal speeds.