A
phase change
In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic State of ...
sometimes occurs when a
wave
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (re ...
is
reflected, 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 waves, sound waves, and waves on 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 "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit tim ...
of , which has the waveformAt 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 waveformsThe continuity condition at the boundary isThis gives the equationsAnd we have the reflectivity and transmissivityWhen , the reflected wave has a reflection phase change of 180°, since . The energy conservation can be verified byThe 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
Medium may refer to:
Science and technology
Aviation
*Medium bomber, a class of war plane
*Tecma Medium, a French hang glider design
Communication
* Media (communication), tools used to store and deliver information or data
* Medium of ...
with higher refractive index
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, or ...
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 (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 oscillations, not the magnetic field 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 Normal(s) or The Normal(s) may refer to:
Film and television
* ''Normal'' (2003 film), starring Jessica Lange and Tom Wilkinson
* ''Normal'' (2007 film), starring Carrie-Anne Moss, Kevin Zegers, Callum Keith Rennie, and Andrew Airlie
* ''Norma ...
incidence—for p-polarized light reflecting off glass at ''glancing'' angle, beyond the Brewster angle
Brewster's angle (also known as the polarization angle) is an angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with ''no reflection''. When ''unpolarized'' light ...
, the phase change is 0°. The phase changes that take place upon reflection play an important part in thin film interference
Thin-film interference is a natural phenomenon in which light waves reflected by the upper and lower boundaries of a thin film interfere with one another, either enhancing or reducing the reflected light. When the thickness of the film is an ...
.
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 SI unit of acoustic impedance is the pascal-second per cu ...
. 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 pitc ...
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 waves on strings, which produce the sound from ]stringed instrument
String instruments, stringed instruments, or chordophones are musical instruments that produce sound from vibrating strings when a performer plays or sounds the strings in some manner.
Musicians play some string instruments by plucking the st ...
s.
The same 180° phase change happens when the wave traveling in a lighter string (lower linear mass density) 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 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
A signal travelling along an electrical transmission line will be partly, or wholly, reflected back in the opposite direction when the travelling signal encounters a discontinuity in the characteristic impedance of the line, or if the far end ...
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
The mobility analogy, also called admittance analogy or Firestone analogy, is a method of representing a mechanical system by an analogous electrical system. The advantage of doing this is that there is a large body of theory and analysis techniq ...
) 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 transmi ...
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 capability of a material object or device 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 ar ...
or inductance will also give rise to a phase shifted wave at full amplitude. The voltage phase shift is given by where
:*''Z''0 is the characteristic impedance of the line
:*''X'' is the susceptance 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 "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit tim ...
.
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 passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a c ...
s and between 0 and −180° for capacitor
A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals.
The effect of ...
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,[
This expression assumes the characteristic impedance is purely ]resistive
The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallels ...
.
See also
*Reflection coefficient
In physics and electrical engineering the reflection coefficient is a parameter that describes how much of a wave is reflected by an impedance discontinuity in the transmission medium. It is equal to the ratio of the amplitude of the reflected w ...
References
{{reflist, 30em
Physical optics
Wave mechanics
Sound