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A phase change sometimes occurs when a
wave In physics, mathematics, engineering, and related fields, a wave is a propagating dynamic disturbance (change from List of types of equilibrium, equilibrium) of one or more quantities. ''Periodic waves'' oscillate repeatedly about an equilibrium ...
is
reflected Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The ...
, specifically from a medium with faster wave speed to the boundary of a medium with slower wave speed. Such reflections occur for many types of wave, including
light wave In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength, ra ...
s,
sound wave In physics, sound is a vibration that propagates as an acoustic wave through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...
s, and waves on vibrating strings.


General theory

For an incident wave traveling from one medium (where the wave speed is ) to another medium (where the wave speed is ), one part of the wave will transmit into the second medium, while another part reflects back into the other direction and stays in the first medium. The amplitude of the transmitted wave and the reflected wave can be calculated by using the continuity condition at the boundary. Consider the component of the incident wave with an
angular frequency In physics, angular frequency (symbol ''ω''), also called angular speed and angular rate, is a scalar measure of the angle rate (the angle per unit time) or the temporal rate of change of the phase argument of a sinusoidal waveform or sine ...
of , which has the waveform u^(x,t) = Ae^;\ A\in \ComplexAt t=0, the incident reaches the boundary between the two mediums at x=0. Therefore, the corresponding reflected wave and the transmitted wave will have the waveforms u^(x,t) = Be^;\ u^(x,t) = Ce^;\ B,C\in \ComplexThe continuity condition at the boundary is u^(0,t)+u^(0,t)=u^(0,t); \ \fracu^(0,t)+\fracu^(0,t)=\fracu^(0,t) This gives the equations A+B=C; \ A-B=\frac C=\frac C And we have the reflectivity and transmissivity \frac=\frac;\ \frac=\frac When , the reflected wave has a reflection phase change of 180°, since . The energy conservation can be verified by \frac+\frac=\frac The above discussion holds true for any component, regardless of its angular frequency of . The limiting case of corresponds to a "fixed end" that doesn't move, whereas the limiting case of corresponds to a "free end".


Optics

Light waves change phase by 180° when they reflect from the surface of a medium with higher
refractive index In optics, the refractive index (or refraction index) of an optical medium is the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refrac ...
than that of the medium in which they are travelling. A light wave travelling in air that is reflected by a glass barrier will undergo a 180° phase change, while light travelling in glass ''will not'' undergo a phase change if it is reflected by a boundary with air. For this reason, optical boundaries are normally specified as an
ordered pair In mathematics, an ordered pair, denoted (''a'', ''b''), is a pair of objects in which their order is significant. The ordered pair (''a'', ''b'') is different from the ordered pair (''b'', ''a''), unless ''a'' = ''b''. In contrast, the '' unord ...
(air-glass, glass-air); indicating which material the light is moving out of, and in to, respectively. "Phase" here is the phase of the
electric field An electric field (sometimes called E-field) is a field (physics), physical field that surrounds electrically charged particles such as electrons. In classical electromagnetism, the electric field of a single charge (or group of charges) descri ...
oscillations, not the
magnetic field A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular ...
oscillations (while the electric field will undergo 180° phase change, the magnetic field will undergo 0° phase change. Vice versa is true when reflection occurs at lower refractive index interface.) Appendix A Also, this is referring to near- normal incidence—for p-polarized light reflecting off glass at ''glancing'' angle, beyond the Brewster angle, the phase change is 0°. The phase changes that take place upon reflection play an important part in thin film interference.


Sound waves

Sound waves in a solid experience a phase reversal (a 180° change) when they reflect from a boundary with air. Sound waves in air do not experience a phase change when they reflect from a solid, but they do exhibit a 180° change when reflecting from a region with lower
acoustic impedance Acoustic impedance and specific acoustic impedance are measures of the opposition that a system presents to the acoustic flow resulting from an acoustic pressure applied to the system. The International System of Units, SI unit of acoustic impeda ...
. An example of this is when a sound wave in a hollow tube encounters the open end of the tube. The phase change on reflection is important in the physics of
wind instrument A wind instrument is a musical instrument that contains some type of resonator (usually a tube) in which a column of air is set into vibration by the player blowing into (or over) a mouthpiece set at or near the end of the resonator. The pitch ...
s.


Strings

A wave on a string experiences a 180° phase change when it reflects from a point where the string is fixed. Reflections from the free end of a string exhibit no phase change. The phase change when reflecting from a fixed point contributes to the formation of
standing wave In physics, a standing wave, also known as a stationary wave, is a wave that oscillates in time but whose peak amplitude profile does not move in space. The peak amplitude of the wave oscillations at any point in space is constant with respect t ...
s on strings, which produce the sound from
stringed instrument In musical instrument classification, string instruments, or chordophones, are musical instruments that produce sound from vibrating strings when a performer strums, plucks, strikes or sounds the strings in varying manners. Musicians play so ...
s. The same 180° phase change happens when the wave traveling in a lighter string (lower linear
mass density Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek language, Greek letter rho), although the Latin letter ''D'' (or ''d'') ...
) reflects off of the boundary of a heavier string (higher linear mass density). This happens because the heavier string doesn't respond as quickly to the tension force as the lighter string, and therefore the amplitude of the oscillation at the boundary point is less than the incoming wave. By the
superposition principle The superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually. So th ...
, the reflected wave must cancel part of the incoming wave, and therefore it is phase shifted. Note that when the wave traveling in a heavier string reflects off of the boundary of a lighter string, since the boundary point has the freedom to move as quickly as possible, no such phase shift would occur in the reflected wave.


Electrical transmission lines

Reflections of signals on conducting lines typically exhibit a phase change from the incident signal. There are two extreme cases of termination: short circuit (closed line), and open circuit (broken line). In both cases the full amplitude of the wave is reflected. ;short circuit: The voltage wave reflection on a line terminated with a short circuit is 180° phase shifted. This is analogous (by the mobility analogy) to a string where the end is fixed in position, or a sound wave in a tube with a blocked off end. The current wave, on the other hand, is not phase shifted. ;broken / open line: A
transmission line In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmis ...
terminated with an open circuit is the dual case; the voltage wave is shifted by 0° and the current wave is shifted by 180°. ;reactive termination: A transmission line terminated with a pure
capacitance Capacitance is the ability of an object to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are two closely related ...
or
inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The electric current produces a magnetic field around the conductor. The magnetic field strength depends on the magnitude of the ...
will also give rise to a phase shifted wave at full amplitude. The voltage phase shift is given by \varphi = 2 \tan ^ where :*''Z''0 is the
characteristic impedance The characteristic impedance or surge impedance (usually written Z0) of a uniform transmission line is the ratio of the amplitudes of voltage and current of a wave travelling in one direction along the line in the absence of reflections in th ...
of the line :*''X'' is the reactance of the inductance or capacitance, given respectively by ''ωL'' or :*''L'' and ''C'' are, respectively, inductance and capacitance, and :*''ω'' is the
angular frequency In physics, angular frequency (symbol ''ω''), also called angular speed and angular rate, is a scalar measure of the angle rate (the angle per unit time) or the temporal rate of change of the phase argument of a sinusoidal waveform or sine ...
. In the case of reactive termination the phase shift will be between 0 and +180° for
inductor An inductor, also called a coil, choke, or reactor, is a Passivity (engineering), passive two-terminal electronic component, electrical component that stores energy in a magnetic field when an electric current flows through it. An inductor typic ...
s and between 0 and −180° for
capacitor In electrical engineering, a capacitor is a device that stores electrical energy by accumulating electric charges on two closely spaced surfaces that are insulated from each other. The capacitor was originally known as the condenser, a term st ...
s. The phase shift will be exactly ±90° when , ''X'', = ''Z''0. For the general case when the line is terminated with some arbitrary impedance, ''Z'', the reflected wave is generally less than the incident wave. The full expression for phase shift needs to be used, \varphi = \tan ^ \left ( \frac \right ) This expression assumes the characteristic impedance is purely resistive.


See also

* Reflection coefficient


References

{{Authority control Physical optics Wave mechanics Sound