traveling waves

Waves.

Optics Series Lecture, Lecture – XII and – XIII

“Traveling waves, Differential wave equations, Particle and wave velocities.”

In one of our earlier optics session lecture I had hinted at having waves defined by their pulse shape called as wave profile — or alternatively wave shape or wave form, and transcribing them into forms that represent actual wave motion.

The later are then called as traveling or progressive waves. The former, the so called wave shape or wave profile are then time-snapshots of the full fledged time varying waves that we just called traveling waves.

Remember that stationary or standing waves are not wave profiles or any snapshots of a single traveling wave, they are rather the superposition of an advanced and a retarded wave — that is one traveling wave moving forward and another exactly shaped traveling wave moving in the reverse direction.

We studied advanced and retarded waves, here.

Harmonic Spherical Waves

Optics Series Lecture, Lecture – X.

“Harmonic Spherical Waves”

This lecture was delivered on 16th February in a lecture session of 1 and 1/2 hours. This lecture was delivered to Physics honors students.

In our lecture ( lecture-VIII ) we worked out the form of plane harmonic traveling waves. Note that soon we will barge into the concept of wave profile and how to convert a wave profile into its corresponding time-dependent or traveling form. But before we do that here is yet another general form of a traveling wave which we often meet in the Physicists Den. The traveling spherical wave fronts. Let us work out its details.

Spherical Waves.
When a stone is dropped in water it sends out circular waves. Similarly a sphere or a glob of matter that oscillates inside of a water body would send out 3-dimensional waves or ripples. Sources of light wave, which we will study in great detail, in this course, to fulfill our insatiable hunger for understanding the nature of optical phenomena, similarly, send out oscillations which propagate radially and uniformly in all directions. These are the spherical waves and the points or region that move out with equal phase are the wave fronts in this case, spherical in shape, called as spherical wave fronts.

We evidently need to describe the spherical wave fronts in spherical polar coordinate system, owing to the spherical symmetry in problems of 3-dimensional propagation of light waves.

Let us recall that the Laplacian in spherical polar coordinate system is given as: