Wave propagation
Encyclopedia
Wave propagation is any of the ways in which waves travel.

With respect to the direction of the oscillation
Oscillation
Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes...

relative to the propagation direction, we can distinguish between longitudinal wave
Longitudinal wave
Longitudinal waves, as known as "l-waves", are waves that have the same direction of vibration as their direction of travel, which means that the movement of the medium is in the same direction as or the opposite direction to the motion of the wave. Mechanical longitudinal waves have been also...

and transverse wave
Transverse wave
A transverse wave is a moving wave that consists of oscillations occurring perpendicular to the direction of energy transfer...

s.

For electromagnetic waves, propagation may occur in a vacuum as well as in a material medium. Most other wave types cannot propagate through vacuum and need a transmission medium
Transmission medium
A transmission medium is a material substance that can propagate energy waves...

to exist.

Another useful parameter for describing the propagation is the wave velocity
Wave velocity
Wave velocity is a wave property, which may refer to:*phase velocity, the velocity at which a wave phase propagates at a certain frequency*pulse wave velocity, the velocity at which a pulse travels through a medium, usually applied to arteries as a measure of arterial stiffness*group velocity, the...

that mostly depends on some kind of density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

of the medium.

## Wave velocity

Wave velocity is a general concept, of various kinds of wave velocities, for a wave's phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...

and speed
Speed
In kinematics, the speed of an object is the magnitude of its velocity ; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance traveled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as...

concerning energy (and information) propagation. The phase velocity
Phase velocity
The phase velocity of a wave is the rate at which the phase of the wave propagates in space. This is the speed at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave will appear to travel at the phase velocity...

is given as:

where:
• vp is the phase velocity (in meter per second
Second
The second is a unit of measurement of time, and is the International System of Units base unit of time. It may be measured using a clock....

, m/s),
• ω is the angular frequency
Angular frequency
In physics, angular frequency ω is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity...

Radian is the ratio between the length of an arc and its radius. The radian is the standard unit of angular measure, used in many areas of mathematics. The unit was formerly a SI supplementary unit, but this category was abolished in 1995 and the radian is now considered a SI derived unit...

s per second, rad/s),
• k is the wavenumber
Wavenumber
In the physical sciences, the wavenumber is a property of a wave, its spatial frequency, that is proportional to the reciprocal of the wavelength. It is also the magnitude of the wave vector...

The phase speed gives you the speed at which a point of constant phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...

of the wave will travel for a discrete frequency. The angular frequency ω cannot be chosen independently from the wavenumber k, but both are related through the dispersion relation
Dispersion relation
In physics and electrical engineering, dispersion most often refers to frequency-dependent effects in wave propagation. Note, however, that there are several other uses of the word "dispersion" in the physical sciences....

ship:

In the special case , with c a constant, the waves are called non-dispersive, since all frequencies travel at the same phase speed c. For instance electromagnetic waves in vacuum
Vacuum
In everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...

are non-dispersive. In case of other forms of the dispersion relation, we have dispersive waves. The dispersion relationship depends on the medium through which the waves propagate and on the type of waves (for instance electromagnetic, sound or water
Ocean surface wave
In fluid dynamics, wind waves or, more precisely, wind-generated waves are surface waves that occur on the free surface of oceans, seas, lakes, rivers, and canals or even on small puddles and ponds. They usually result from the wind blowing over a vast enough stretch of fluid surface. Waves in the...

waves). For sound waves, the denser a medium is, the faster the waves will travel as particles will be closer together and thus energy can be transferred among them at a greater rate.

The speed at which a resultant wave packet from a narrow range of frequencies will travel is called the group velocity
Group velocity
The group velocity of a wave is the velocity with which the overall shape of the wave's amplitudes — known as the modulation or envelope of the wave — propagates through space....

and is determined from the gradient
In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....

of the dispersion relation
Dispersion relation
In physics and electrical engineering, dispersion most often refers to frequency-dependent effects in wave propagation. Note, however, that there are several other uses of the word "dispersion" in the physical sciences....

:

In almost all cases, a wave is mainly a movement of energy through a medium. Most often, the group velocity is the velocity at which the energy moves through this medium.

• Absorption (electromagnetic radiation)
In physics, absorption of electromagnetic radiation is the way by which the energy of a photon is taken up by matter, typically the electrons of an atom. Thus, the electromagnetic energy is transformed to other forms of energy for example, to heat. The absorption of light during wave propagation is...

• Antenna theory
• Diffraction
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...

• Huygens–Fresnel principle
• Photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

• Polarization (waves)
Radio propagation is the behavior of radio waves when they are transmitted, or propagated from one point on the Earth to another, or into various parts of the atmosphere...

• Reflection (physics)
Reflection (physics)
Reflection is the change in direction of a wavefront at an interface between two differentmedia so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves...

• Refraction
Refraction
Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...

• Scattering
Scattering
Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of...

• Wave
Wave
In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...