Below you will find example sentences with "wave equation". The examples show how this phrase is used in natural context and which words often surround it.

Wave Equation in a sentence

Corpus data

  • Displayed example sentences: 20
  • Discovered as a combination around: wave
  • Corpus frequency in the collocation scan: 8
  • Phrase length: 2 words
  • Average sentence length: 27 words

Words in this phrase

wave equation

Meanings of words in this phrase

  • wave can mean: To move back and forth repeatedly and somewhat loosely. Frequent word
  • equation can mean: The act or process of equating two or more things, or the state of those things being equal (that is, identical). Frequent word

Sentence profile

  • Phrase position: 4 start, 11 middle, 5 end
  • Sentence types: 20 statements, 0 questions, 0 exclamations

Usage patterns

These patterns show short text windows around the phrase in the example sentences:

applying the wave equation to the 1× dimensional waves wave equation main consider 1× dimensions the wave equation is we 1× discovered the wave equation in one 1× equation the wave equation in one 1× follow the wave equation which are 1× for the wave equation in three 1× frequency domain wave equation for a 1×

Sentence openings and endings

Common sentence openings:

scalar wave equation 2× a more general 1× a solution of 1× although the word 1× an observation or 1× ballentine points out 1×

Common sentence endings:

the wave equation 2× a spherical wave 1× and the object 1× different physical settings 1× dimensional delta function 1× dimensional wave equation 1×

Context words

These words often appear near this phrase in the example sentences:

space 6× dimensional 6× solutions 6× dimensions 5× dimension 4× waves 4× solution 4× electromagnetic 4× form 3× general 3× source 3× frequency 3×

Related phrases

first wave shock wave plane wave standing wave tropical wave

Phrases around this combination

Other phrases discovered around wave:

first wave 17× plane wave 9×

Just before it in the phrase index:

waters off water utility water usage water treatment water tank water supply

Just after it in the phrase index:

wavelet transform wayne county wayne ind weak topology wealth advisors wealth creation

Corpus analysis

  • The phrase "wave equation" has 2 words and usually appears in the middle in these examples. The average sentence has 27 words and is mostly made up of statements.
  • Around this phrase, patterns and context words such as applying the wave equation to the, dimensional waves wave equation main consider, space, dimensional and solutions stand out.
  • In the phrase index, this combination connects with first wave, shock wave, plane wave, first wave and plane wave, linking the page to nearby combinations.

Example types with wave equation

This selection groups the examples by length and sentence type, making usage of the full phrase easier to scan:

Short example sentences

Thus, this equation is sometimes known as the vector wave equation. (11 words)

For particles with mass this equation has solutions that follow the form of the wave equation. (16 words)

The field permits solutions that follow the wave equation, which are referred to as the wave functions. (17 words)

Longer example sentences

Scalar wave equation in two space dimensions In two space dimensions, the wave equation is : We can use the three-dimensional theory to solve this problem if we regard u as a function in three dimensions that is independent of the third dimension. (43 words)

General aperture The wave that emerges from a point source has amplitude at location r that is given by the solution of the frequency domain wave equation for a point source (The Helmholtz Equation ), : where is the 3-dimensional delta function. (41 words)

To obtain a solution with constant frequencies, let us first Fourier transform the wave equation in time as : So we get, : This is the Helmholtz equation and can be solved using separation of variables. (34 words)

Example sentences (20)

Derivation of the wave equation The wave equation in one space dimension can be derived in a variety of different physical settings.

For such waves, the three-dimensional wave equation takes the form : This is equivalent to : and hence the quantity ru satisfies the one-dimensional wave equation.

General aperture The wave that emerges from a point source has amplitude at location r that is given by the solution of the frequency domain wave equation for a point source (The Helmholtz Equation ), : where is the 3-dimensional delta function.

Scalar wave equation in one space dimension French scientist Jean-Baptiste le Rond d'Alembert (b. 1717) discovered the wave equation in one space dimension.

Scalar wave equation in two space dimensions In two space dimensions, the wave equation is : We can use the three-dimensional theory to solve this problem if we regard u as a function in three dimensions that is independent of the third dimension.

For particles with mass this equation has solutions that follow the form of the wave equation.

Thus, this equation is sometimes known as the vector wave equation.

To obtain a solution with constant frequencies, let us first Fourier transform the wave equation in time as : So we get, : This is the Helmholtz equation and can be solved using separation of variables.

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A solution of the initial-value problem for the wave equation in three space dimensions can be obtained from the corresponding solution for a spherical wave.

Ballentine points out that whilst it is arguable to associate a physical wave with a single particle, there is still only one Schrödinger wave equation for many particles.

Mathematical description of one-dimensional waves Wave equation main Consider a traveling transverse wave (which may be a pulse ) on a string (the medium).

Physically one gets the normal electromagnetic wave solutions to the homogeneous part of the wave equation: : and the inhomogeneous term : acts as a driver/source of the electromagnetic waves.

The field permits solutions that follow the wave equation, which are referred to as the wave functions.

The Hankel functions are used to express outward- and inward-propagating cylindrical wave solutions of the cylindrical wave equation, respectively (or vice versa, depending on the sign convention for the frequency ).

Therefore, there are solutions in the form : where F and G are general solutions to the one-dimensional wave equation, and can be interpreted as respectively an outgoing or incoming spherical wave.

Under these conditions, the electric and magnetic fields satisfy the electromagnetic wave equation : Field and Wave Electromagnetics (2nd Edition), David K. Cheng, Prentice Hall, 1989.

Although the word "monochromatic" is not exactly accurate since it refers to light or electromagnetic radiation with well-defined frequency, the spirit is to discover the eigenmode of the wave equation in three-dimensions.

A more general representation of the wave equation is more complex, but the role of amplitude remains analogous to this simple case.

An observation or measurement of an object by an observer is modeled by applying the wave equation to the entire system comprising the observer and the object.

Both types of waves can have a waveform which is an arbitrary time function (so long as it is sufficiently differentiable to conform to the wave equation).

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