what is the meaning of wave propagation?

Answer 1

Wave Propagation:

Ultrasonic testing is based on time-varying deformations or vibrations in materials, which is generally referred to as acoustics. All material substances are comprised of atoms, which may be forced into vibrational motion about their equilibrium positions. Many different patterns of vibrational motion exist at the atomic level, however, most are irrelevant to acoustics and ultrasonic testing. Acoustics is focused on particles that contain many atoms that move in unison to produce a mechanical wave. When a material is not stressed in tension or compression beyond its elastic limit, its individual particles perform elastic oscillations. When the particles of a medium are displaced from their equilibrium positions, internal (electrostatic) restoration forces arise. It is these elastic restoring forces between particles, combined with inertia of the particles, that leads to oscillatory motions of the medium.

In solids, sound waves can propagate in four principle modes that are based on the way the particles oscillate. Sound can propagate as longitudinal waves, shear waves, surface waves, and in thin materials as plate waves. Longitudinal and shear waves are the two modes of propagation most widely used in ultrasonic testing. The particle movement responsible for the propagation of longitudinal and shear waves is illustrated below.

In longitudinal waves, the oscillations occur in the longitudinal direction or the direction of wave propagation. Since compressional and dilational forces are active in these waves, they are also called pressure or compressional waves. They are also sometimes called density waves because their particle density fluctuates as they move. Compression waves can be generated in liquids, as well as solids because the energy travels through the atomic structure by a series of comparison and expansion (rarefaction) movements.

In the transverse or shear wave, the particles oscillate at a right angle or transverse to the direction of propagation. Shear waves require an acoustically solid material for effective propagation and, therefore, are not effectively propagated in materials such as liquids or gasses. Shear waves are relatively weak when compared to longitudinal waves In fact, shear waves are usually generated in materials using some of the energy from longitudinal waves.

Answer 2

Man - those other answers are probably better and more comprehensive if you can actually read them. Wave propagation is the act of a wave continuing onward and outwards - Simplest analogy is a pebble thrown into a still pond and the wave wripples keep 'propagating outwards'.

Answer 3

Okay...

This set of words has to do with the way energy radiates outward from a source.

Doesn't matter if the source is the muzzle of a gun,
a pebble striking the surface of the water, a radio transmitting antenna, a light bulb, or a loud speaker.

Energy is somehow released at the source and radiates outward in waves. How those waves travel away from the source, and at what speed they travel is generaly called wave propagation.

For example:
Sound waves die out rather quickly in air, but travel for vast distances in solids.

Sound waves bounce off of solid objects such as canyon walls (creates echoes), but pass right through porus objects like trees, leaves, rain showers.

If the source of the energy is a "point source" with the identical environment on all sides, then the energy radiates outward in rings of ever expanding diameters.
As the rings expand, the energy within them decreases.
Example: The brightness of a flashlight illuminated card will decrease as you move the card farther and farther away from the flashlight. The rate of decrease is normaly a function of the square of the distance from the source.
Another factor to be aware of is the transmission index of the medium the wave (light) is passing through. Some mediums slow down a wave, some let it pass through with little or no influence whatsoever. Some mediums reflect part of the wave (or most of the wave) back towards its source (or off at an angle).

If your waves were radio waves, I could tell you that some radio waves travel for long distances on direct paths
while others (depending upon the frequency of the radio wave) travel only short distances. Relatively low radio frequency waves also bounce off of the ionisphere and return to earth while very high frequency radio waves penetrate through the ionisphere and keep right on going with no apparent reflection.

The bouncing effect off of the ionisphere is called (by radio buffs) "skip". Certain sections of the radio spectrum are prone to good skip conditions and others are seldom influenced by skip. This discussion requires more space than I have here to discuss. Refer to the ARRL Radio Amateurs Handbook for more information on this subject.