standing waves on a cylindrical jet as we know, there are some perturbations on a falling jet which are always present and according to their wave number and the radius of the jet, they can grow and decay over time. so, imagine a jet which has those sort of long wavelength waves traveling downward on it, we put an obstacle on the path of the jet and then we would see this : 

so, what exactly happens to those waves by the presence of an obstacle? 
why have those waves been too larger in amplitude and too short in wavelength in presence of an obstacle?
This photo has taked by sayyedali.m.(  Qom)in Shahid qodosi high school
 A: You're seeing the effects of a capillary instability of the jet, known as the Rayleigh instability (sometimes also as the Rayleigh-Plateau instability) which is largely driven by surface tension effects. The technical details are nontrivial, however. A rough overview of the phenomenon is on Wikipedia, a detailed account is given in this book chapter on Springer Link (it looks like the chapter is freely available for download).
Notice that the instability is characterized by a broad spectrum of unstable wavenumbers, see this figure:

Thus the specific wavenumber you observe can be significantly affected by initial and boundary conditions. The waves in the image you show are unusually short for this instability (maximum amplification for the inviscid case is for a wavelength of roughly 4.5 times the diameter of the jet; this increases with viscosity). My guess is that in this case surface waves at the point of impact of the jet excite shorter-wavelength disturbances.
P.S.: An extensive discussion of the physics of liquid jets is here, including downloadable PDF article.
