Such collision launches compressional transient, rather broadband, which has no specific wavelength, but a spatial width. This width is determined by the time of interaction between 2 bodies and the speed of sound in the target, t*V. The stiffer materials are, the shorter the interaction time.

This is not a 1D situation due to the small dimensions of the nose (or diameter) of the projectile. Next to the interacting surfaces rarefaction waves will overtake the compression wave very  soon. What remains is largely elastic waves reflecting from the free surfaces of the ceramic tile. 

Well, as E.C. has correctly mentioned, in case the problem becomes 3D, the acoustic pulse becomes more complex. This happens at a distance greater than the diffraction length (great enough compared to the nose size). Low frequency part of the pulse undergoes strong divergency (or diffraction), and thus decreases in magnitude. The pulse becomes bipolar. As for the reflection from the free surface, I doubt that. The surface is not free in the collision area, there is stress applied, and another solid is coupled. So the reflection would depend on the acoustic impedances of both solids.

Let us say that the resulting wavelength is longer than V*t, up to 2*V*t if the bullet material is soft.

As the nose (and diameter) of the projectile are small compared to the size of the ceramic target, the area next to the impact zone (just outside the collision area) is a free surface. It may experience elastic waves (such as a Rayleigh wave), but these result mainly in out-of-plane movements as the pressure remains 1 bar (as the pressure remains equivalent at each material interface). This is the reason rarefaction waves kick in that will interfere with the compressive wave (caused by the impact of the projectile).

So the intensity of the impact induced compression wave is reduced by two mechanisms: divergence and release waves from the free surface (just outside the impacted area).  

Yes, I agree that the surface waves are excited efficiently by such impact. I only want to mention that Rayleigh waves are decoupled from the bulk waves, and have no influence on the shape of the bulk transient. Leaky surface-skimming bulk waves contribute to the acoustic field in the bulk, but weakly.

Besides these waves, bulk shear waves are excited as well, if the nose is small.

shock waves caused by an impactor is supposed to "shock" all the material it passes and the particle velocity behind the shock wave front can be infinitely thick if the projectile and target are thickness. When we talk about wavelength, we are talking the perodical distribution of particle velocity over the wavelength space. In this sense, the wavelength can be very large. Howver, for impactor-target system of finite dimension, tranmission and reflections from various interface interact and producing temperory spacial pattern with certain characteristic length. You can use such characteristic length as an estimate of the wavelength which shall be in the same oredr of mangnitude as the geometric parameters such as target thickness, impactor diameter or length. Do use such "wavelength" carefully.

In order to generate a shock wave in the target one should use a flat impactor of large diameter, otherwise rarefaction waves will run in from behind the shock wave and reduce its intensity, hence propagation velocity, shock front shape, etc.  

Impact of a small object on a large surface only leads to a curved shockwave that is reducing in intensity very fast due to its divergence (3D expansion) as well as rarefaction waves that rum in from behind (originated from the free surface adjacent to the impact area). Very soon the intensity of the wave is reduced to the elastic range (sound waves) that do not show a (residual) particle velocity and are sonic rather than supersonic.  

As most projectiles in ballistics have small diameters compared to the target materials, and many projectiles possess sharp noses, the interaction area is very small. This creates largely an elastic/plastic loading condition for the material. Shock wave physics play only a small role in such interactions.

In 1914, B. Hopkinson [1] gave an estimation of the duration of the projectile-target interaction with an estimation of the pressure induced temporal profile. According to him, the duration of the interaction depends on the projectile geometry (as a rigid body, so it comes true for Armor Piercing ammunitions). If L is the mass per unit of length along the projectile, and v0 the initial velocity, each element of the projectile suffers the impact pressure P=L*v0^2. He estimate the duration tho as the time taken by the bullet to enter entirely in the target, thus tho=lenght_proj*projectile_velocity.

Under these considerations, the wavelength is the sound velocity of the target * tho.

I would personnaly prefer a shock polar approach that will also considers the material velocity induced by the imapct both in the target and projectile. It is a 1D approach that does not take into account lateral waves also called edge effects [2].

Another possibility is to consider the contact theory of Hertz that gives a contact duration estimation that is applied to ballistic impacts by Hutchins for instance [3] : tho=Pi*wp where wp the plastic pulsation that is expressed by wp= (1/r)√(3Pmax/2ρ) for a sphere of radius r, a target of density rho and a max pressure loading of Pmax.

Refs:

[1] Hopkinson, B. (1914). A method of measuring the pressure produced in the detonation of high explosives or by the impact of bullets. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 213(497-508), 437-456.

[2] Boustie, M., Cuq-Lelandais, J. P., Bolis, C., Berthe, L., Barradas, S., Arrigoni, M., ... & Jeandin, M. (2007). Study of damage phenomena induced by edge effects into materials under laser driven shocks. Journal of Physics D: Applied Physics, 40(22), 7103.

[3] Hutchings, I. M. (1983). The behaviour of metals under ballistic impact at sub-ordnance velocities. In Material Behavior under High Stress and Ultrahigh Loading Rates (pp. 161-196). Springer, Boston, MA.