Waves

Interference is a phenomenon which concerns waves. The occurrences concerning waves are less intuitive than the ones concerning material particles. However it is necessary to become conversant with them, at least at a level which allows us a satisfactory comprehension of the single electron interference experiment.

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Waves created inside the fountain located in the garden of the old Bologna seat of the National Research Council, Via de’ Castagnoli 1, presently seat of the Bologna Education Office. The scene is taken from the initial part of the 1976 movie “Electron Interference”.

Types of waves: mechanical waves

Let us start with examples of “mechanical waves”

First of all, what is a mechanical wave? It is a perturbation or, more simply, a motion, elicited by a trigger of some kind, which propagates through a material medium, involving in the motion of areas further and further apart from that in which it was generated. For instance a wave can be generated in a stretched string fixed at one end if the other end is made to oscillate, or when one liquid drop or a stone is dropped on a water surface, and a wave is involved when we listen to a sound moving through the air. In the first case we are dealing with a one-dimensional wave since the perturbation is propagating along one direction, the direction of the stretched string (but the sections of the string oscillate in a direction perpendicular to that of wave propagation); in the second case we have a two-dimensional wave since the wave propagates in all directions on the water surface (even here, we can observe that the water particles oscillate in a direction perpendicular to the one of wave propagation), while in the third case the wave is three-dimensional since the oscillations of the molecules of the air propagate in all directions in the space surounding the source (in this case oscillations occur in the same directions of wave propagation, for short steps, giving rise to alternate areas of “thickening” and “rarefaction” of the air with respect to the unperturbed equilibrium situation.

The more the wave propagates, the more it becomes damped. Thus, a certain time after the fall of a stone, the water of a pond returns to stillness. We notice that in the case of a wave it is not possible to talk about position or trajectory, at variance with what happens with material particles, even though we can follow the shift of a wavefront (for instance a circumference in the case of circular waves on water).

Animation of a one-dimensional wave propagating on a stretched string. The trigger action in this case is a quick motion imparted to the free end of the string (dark dot) moving it upward and then bringing it back to the rest position. Animation courtesy of Dr. Dan Russell, Kettering University.

Generation of a wave in a stretched string

Generation of a succession of waves, or wave “train” on a string.

Slow-motion sequence of circular (two-dimensional) waves produced on a water surface by the fall of a drop (reproduced from the site www.acoustics.salford.ac.uk).

The waves produced by the wind on the Trasimeno Lake are an example of two-dimensional waves, with approximately rectilinear wavefronts (Photo by M. Gagliardi)

Here we have an example of rectilinear waves produced in a ripple tank , an educational device we will encounter later on.

The sound is the result of pressure waves propagating through the air. When they reach the ear, they induce a vibration in the eardrum, which in turn transmits the vibration to the organs of the internal ear, up to the acoustic nerve which sends to the brain a signal, the elaboration of which originates the sound sensation. In the absence of a medium (as is the case of the empty space beyond the atmosphere) it is not possible to hear sounds, no matter how often this basic fact of physics might be ignored in many science fiction movies.

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