There is one fundamental equation that describes sound wave propagation, but the phenomena that emerge from it are varied and often complex.

The acoustic wave equation is a combination of these two sets of balance equations and can be expressed as

The acoustic wave equation ( and the mass and momentum balance equations ) are often expressed in terms of a scalar potential where.

In that case the acoustic wave equation is written as

This assumption leads to the linear or small signal acoustic wave equation.

Then the solution of the acoustic wave equation is

Dirac realised that his relativistic version of the Schrödinger wave equation for electrons predicted the possibility of antielectrons.

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 ).

Swiss physicist Felix Bloch provided a wave function solution to the Schrödinger equation with a periodic potential, called the Bloch wave.

Once the electronic and nuclear variables are separated ( within the Born – Oppenheimer representation ), in the time-dependent approach, the wave packet corresponding to the nuclear degrees of freedom is propagated via the time evolution operator ( physics ) associated to the time-dependent Schrödinger equation ( for the full molecular Hamiltonian ).

His work was a key aspect of Hermann Weyl and John von Neumann's work on the mathematical equivalence of Werner Heisenberg's matrix mechanics and Erwin Schrödinger's wave equation and his namesake Hilbert space plays an important part in quantum theory.

There are various analytical models which allow the diffracted field to be calculated, including the Kirchhoff-Fresnel diffraction equation which is derived from wave equation, the Fraunhofer diffraction approximation of the Kirchhoff equation which applies to the far field and the Fresnel diffraction approximation which applies to the near field.

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 ),

Because the speed of EM waves predicted by the wave equation coincided with the measured speed of light, Maxwell concluded that light itself is an EM wave.

MWI treats the other histories or worlds as real since it regards the universal wavefunction as the " basic physical entity " or " the fundamental entity, obeying at all times a deterministic wave equation ".

It can be shown, that, under these conditions, the electric and magnetic fields satisfy the electromagnetic wave equation:

The fundamental frequency of a sound wave in a tube with a single CLOSED end can be found using the following equation:

The fundamental frequency of a sound wave in a tube with either BOTH ends OPEN or CLOSED can be found using the following equation:

* solutions of the Schrödinger wave equation

The observed intensity of the radio emission of Venus is much higher than the expected thermal intensity, although the spectrum indicated by measurements at wave lengths near 3 cm and 10 cm is like that of a black body at about 600-degrees.

Mars has been observed twice at about 3-cm wave length, and the intensity of the observed radiation is in reasonable agreement with the thermal radiation which might be predicted on the basis of the known temperature of Mars.

No attempts to measure the radio emission of the remaining planets have been reported, and, because of their distances, small diameters, or low temperatures, the thermal radiation at radio wave lengths reaching the earth from these sources is expected to be of very low intensity.

The radio radiation of the sun which is reflected from the moon and planets should be negligible compared with their thermal emission at centimeter wave lengths, except possibly at times of exceptional outbursts of solar radio noise.

An ordinary sea wave is rarely more than a few hundred feet long from crest to crest -- no longer than 320 feet in the Atlantic or 1,000 feet in the Pacific.

The greater the depth of the water, the greater is the speed of the wave ; ;

Generally the first salvo of a tsunami is a rather sharp swell, not different enough from an ordinary wave to alarm casual observers.

A tsunami is not a single wave but a series.

The waves are separated by intervals of 15 minutes to an hour or more ( because of their great length ), and this has often lulled people into thinking after the first great wave has crashed that it is all over.

The `` moving '' picture of the train or the wave coming at the audience is, to be sure, more intense than a still picture of the same subject, but the difference is really one of degree ; ;

-- A wave of public resentment against corruption in government is rising in Massachusetts.

This is mainly due to the immigration wave of the 1990s.

Amplitude modulation ( AM ) is a technique used in electronic communication, most commonly for transmitting information via a radio carrier wave.

This is used by radio amateurs to transmit Morse code and is known as continuous wave ( CW ) operation.

Aristotle ( 384-322 BC ) understood that sound consisted of contractions and expansions of the air " falling upon and striking the air which is next to it ...", a very good expression of the nature of wave motion.

The central stage in the acoustical process is wave propagation.

The lowest possible energy an electron can take is therefore analogous to the fundamental frequency of a wave on a string.

) A state is actually a function of the coordinates of all the electrons, so that their motion is correlated, but this is often approximated by this independent-particle model of products of single electron wave functions.

Fundamentally, an atomic orbital is a one-electron wave function, even though most electrons do not exist in one-electron atoms, and so the one-electron view is an approximation.

If wave function collapse is regarded as ontologically real as well, an objective collapse theory is obtained.

F wave persistence is the number of F waves obtained per the number of stimulations, which is normally 80-100 % ( or above 50 %).

After the measurement is performed, having obtained some result x, the wave function collapses into a position eigenstate centered at x.

The equation alone does not specify a solution ; a unique solution is usually obtained by setting a problem with further conditions, such as initial conditions, which prescribe the value and velocity of the wave.

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

According to this view, the story of Jacob's visit to Laban to obtain a wife began as a metaphor for the second migration, with Jacob's new family, possessions, and livestock, obtained from Laban, being representations of the new wave of migrants ;

His work in chromatic polarization and rotary polarization greatly advanced the field of optics, although it was later shown that his findings could also be obtained using the wave theory of light ( Frankel ).

When fed with an RF current at the resonant frequency, the quarter wave element contains a standing wave with the voltage and current largely ( but not exactly ) in phase quadrature, as would be obtained using a quarter wave stub of transmission line.

Pressure Recording Analytical Method ( PRAM ), estimates Q from the analysis of the pressure wave profile obtained from an arterial catheter ( radial or femoral access ).

Though there were no allegations that Koch obtained any financial benefit from the corruption, the wave of scandals undermined Koch's prior claims that he would run a patronage-free city government.

According to this view, the story of Jacob's visit to Laban to obtain a wife began as a metaphor for the second migration, with Jacob's new family, possessions, and livestock, obtained from Laban, being representations of the new wave of migrants ; it is notable that, according to textual scholars, in the Jahwist version of the story it is only the Joseph tribes that are among these migrants, since it only recounts Jacob as having met Rachel, and the matriarchs of the other Israelite tribes-Leah, Bilhah, and Zilpah-do not appear.

However, since the development of computational chemistry, the LCAO method often refers not to an actual optimization of the wave function but to a qualitative discussion which is very useful for predicting and rationalizing results obtained via more modern methods.

Major pieces of work which he did coauthor dealt with applications of ( 1 ) group theory in band structure calculations and ( 2 ) equivalent features of linear combination of atomic orbital ( LCAO ), tight binding and Bloch wave approximations, to interpolate results for the energy levels of solids, obtained by more accurate methods,

An impression of the dispersive behaviour of this wave packet is obtained by looking at

Decomposing the initial disturbance in these modes he obtained the Fourier spectrum of the resulting wave.

In part VI of his 1864 paper " Electromagnetic theory of light ", Maxwell combined displacement current with some of the other equations of electromagnetism and obtained a wave equation with a speed equal to the speed of light.

The basic principle of the correlative interferometer consists in comparing the measured phase differences with the phase differences obtained for a DF antenna system of known configuration at a known wave angle ( reference data set ).

After a wave of protests, he was discharged and permitted to immigrate to the USA where he obtained the position of professor of mathematics.

Compressed-gas driven shock tubes are more easily obtained and maintained in laboratory conditions ; however, the shape of the pressure wave is different from a blast wave in some important respects and may not be suitable for some applications.

A 50 % duty cycle square wave is easily obtained by noting whether the capacitor is being charged or discharged, which is reflected in the current switching comparator output.