What is Phase difference: Definition and 162 Discussions
In physics and mathematics, the phase of a periodic function
F
{\displaystyle F}
of some real variable
t
{\displaystyle t}
(such as time) is an angle-like quantity representing the fraction of the cycle covered up to
t
{\displaystyle t}
. It is denoted
ϕ
(
t
)
{\displaystyle \phi (t)}
and expressed in such a scale that it varies by one full turn as the variable
t
{\displaystyle t}
goes through each period (and
F
(
t
)
{\displaystyle F(t)}
goes through each complete cycle). It may be measured in any angular unit such as degrees or radians, thus increasing by 360° or
2
π
{\displaystyle 2\pi }
as the variable
t
{\displaystyle t}
completes a full period.This convention is especially appropriate for a sinusoidal function, since its value at any argument
t
{\displaystyle t}
then can be expressed as the sine of the phase
ϕ
(
t
)
{\displaystyle \phi (t)}
, multiplied by some factor (the amplitude of the sinusoid). (The cosine may be used instead of sine, depending on where one considers each period to start.)
Usually, whole turns are ignored when expressing the phase; so that
ϕ
(
t
)
{\displaystyle \phi (t)}
is also a periodic function, with the same period as
F
{\displaystyle F}
, that repeatedly scans the same range of angles as
t
{\displaystyle t}
goes through each period. Then,
F
{\displaystyle F}
is said to be "at the same phase" at two argument values
t
1
{\displaystyle t_{1}}
and
t
2
{\displaystyle t_{2}}
(that is,
ϕ
(
t
1
)
=
ϕ
(
t
2
)
{\displaystyle \phi (t_{1})=\phi (t_{2})}
) if the difference between them is a whole number of periods.
The numeric value of the phase
ϕ
(
t
)
{\displaystyle \phi (t)}
depends on the arbitrary choice of the start of each period, and on the interval of angles that each period is to be mapped to.
The term "phase" is also used when comparing a periodic function
F
{\displaystyle F}
with a shifted version
G
{\displaystyle G}
of it. If the shift in
t
{\displaystyle t}
is expressed as a fraction of the period, and then scaled to an angle
φ
{\displaystyle \varphi }
spanning a whole turn, one gets the phase shift, phase offset, or phase difference of
G
{\displaystyle G}
relative to
F
{\displaystyle F}
. If
F
{\displaystyle F}
is a "canonical" function for a class of signals, like
sin
(
t
)
{\displaystyle \sin(t)}
is for all sinusoidal signals, then
φ
{\displaystyle \varphi }
is called the initial phase of
For a parallel RLC circuit, I have found the complex impedance to be 1/ (1/R -j(1/wL +wC)) . I need to find the phase difference between the voltage and current in the circuit. I know it's given by tan^-1(im(z)/re(z)) but how do I do it here as the expression is a fraction?
I understand the equation (path difference)/wavelength x 2pi = phase difference, but in this case I do not know how changing the distance of H from the source will affect the path difference. In addition to this, does minima refer to 0 amplitude (complete destructive interference) or does minima...
Hello! This question is in relation to parity violation (PV) measurements using the optical rotation technique (I can give more details/references about that, but most of it is not relevant for my question). Basically, in a simplified model, they have 2 levels (say of positive parity), g and...
how does capacitors and inductors cause phase difference between current and voltage? how does complex number come into play to explain the relation between phase of current and voltage?
I want to locate an infrared signal using Angle on arrival (AoA), I have elected to use Phase Interferometry to achieve this, I am however struggling to understand how the phase difference (∆ϑ) is found. Can someone explain how I could find this?
Consider a circuit with a witch, capacitor and an AC voltage source.
The sinusoidal AC voltage source is depicted in the following graph:
We know that, ##Q = CV##
##\frac{dQ}{dt} = C \frac{dV}{dt}##
##i = C\frac{dV}{dt} \tag{1}##
So from the graph, the voltage increases rapidly around ## t =...
So to do this problem I need the relevant formula for phase difference which is this:
I first need to find wavelength and this is lambda = velocity/frequency
So lambda = 257/641 = 0.40093603744 m
Hence phase difference (in radians) = 2pi * (2/0.40093603744) = 31.3 rads
My concern is that...
See fig(a), S1Q=7lambda
S2Q=9lambda
I think since source S2 is lagging behind. So, we should add the phase 4pi instead of subtracting it from the cosine function. Wouldn't subtracting the phase further delay the wave more.
I had to find the phase difference between sound waves created by two sources at different distances from a given point. I found the correct answer to be about 13.4.
Would any other answer of the form (13.4 + 2npi) also be correct, assuming n is a non-zero integer? Or is 13.4 the only correct...
Homework Statement
Parallel water waves of wavelength 10 m strike a straight sea wall. The wavefronts make an angle 30o with the wall. What is the difference in phases between the waves at two points 5 m apart along the wall?
a. 30o
b. 45o
c. 90o
d. 156o
e. 180o
Homework Equations
Δφ = Δx / λ...
Homework Statement
Derive the relationship bewteen x_{max}, A_{+}, A_{-} and \phi
Homework Equations
x(t) = e^{\gamma t}(A_{+}e^{i \omega_d t} + A_{-}e^{-i \omega_d t})
x(t) = x_{max} e^{\gamma t} cos(\omega_d t + \phi)
The Attempt at a Solution
I know the e^{\gamma t} cancels and for the...
Homework Statement
In a Newton's rings apparatus, find the phase difference (in radians) when an air wedge of 500nm thickness is illuminated with red light (lambda = 640nm).
t = 500nm
lambda = 640nm
radians = degrees × pi / 180°
Answer) 13
Homework Equations
2pi x path difference / lambda...
Today I took two coils and connected one of them (coil A) to an AC power supply. I held the second coil (coil B) close to the first one and then connected them both to a dual trace CRO. As expected, an emf was induced in coil B and the traces on the scope were 90 degrees out of phase. As I...
and Homework Statement
Ok, so I am doing As physics at the moment and have been left confused by stationary waves.
I have read that between adjacent nodes/ even numbers the phase difference is always 0 and between numbers of does it is pi radians. So in the attatched image why is my textbook...
Q1:
So I'm trying to extract the electrical properties of a single phase induction motor. First off, how am I supposed to measure the phase difference between the start and run windings? I have L and R of start and run windings too!
Q2:
I have a torque vs slip curve up until 130% of rated load...
Homework Statement
An inductor (Xl = 40.2 ohm) is connected in series with a resistance (30 ohm) and and an AC source ( 10V , 80Hz) and the current flows in this circuit is 0.2 amp. How could you reduce the phase difference between current and voltage to zero without changing the value of...
Homework Statement
State the phase relationship between
x and y
x and z
(shown in photo)
The Attempt at a Solution
I got the phase difference between x and y to be 135 degrees and then between x and z to be 45 degrees. However the mark scheme gives the answers 180 degrees and 0 degrees. Please...
Hi, would it be possible to explain to me how does wave length, phase difference and path difference all link as I'm struggling with calculations involving these three things.
Homework Statement
Hello,
For two waves to be coherent, they must have the same frequency right? Does this on its own implies a constant phase different between any point on one wave and any on the other.
So, for example, if we had two waves with different wavelengths and velocities but equal...
Homework Statement
The two oscillators each have the same mass. Use Fig. 4.1 to determine (i) the phase difference between the two oscillators (picture attached)
Homework Equations
Subtracting to find the horizontal shift
The Attempt at a Solution
I found the two points where both graphs...
If i have two sinusoidal ac signals of 220V with the different phase angle i.e. there is some phase difference between them. Then can i make the phase difference zero?? Please tell
When solving the differential equations for an electromagnetic wave you get out that the electric and magnetic field oscillate in phase.
But when considering a oscillating dipole, the electric and magnetic field at a point close to the dipole are a quater period out of phase.
Can someone please...
Homework Statement
[/B]
imgur: http://i.imgur.com/9ktFGSs.pngHomework EquationsThe Attempt at a Solution
[/B]
I came up with both 150 and 210 as the difference between the phase angles. I chose 150.
If you draw the vectors and compare their angles, the angular difference between them could...
Hi so I am wondering about potential phase difference in some 110v 60 hz household wiring... Say I have two switches to control one light and am too cheap to buy 3 way switches. If I were to run power from switch 1 to switch 2 (bypassing switch 1), so that they both had power at the switch, if I...
Why will it happen so that-two light sources such that the
''phase difference between the two vibrating sources changes
rapidly with time, we say that the two sources are incoherent and when
this happens the intensities just add up ''
assuming that the wave characteristics of light are significant
Homework Statement
Three receivers, with complex impedance \underline{Z_1}=(125+j375)\Omega,\underline{Z_2}=(700+j100)\Omega,\underline{Z_3}=(500-j500)\Omega, and two sinusoidal current generators of effective values I_{g2}=40mA and unknown I_{g1} are connected. When the switch is open...
Homework Statement
A plane-wave is incident on an air-glass interface at 30° as shown below. Calculate the phase difference between A and B. Assume λo=1μm.
attatched is an image that looks like this.
________________________
--------------------------- A
--------------------------- B...
Homework Statement
In a double slit experiment, the distance between the slits is 0.2mm and the distance to the screen is 150cm. What is the phase difference in degrees, between the waves from the two slits arriving at point P, when the angular distance of P is 10 degrees relative to the...
Homework Statement
Light of a wavelength 548nm illuminates two slits separated by 0.25mm. At what angle would one find the phase difference between the waves from two slits to be 2 rads?
Homework Equations
σ / λ = ΔΦ / 2π
σ: path difference
λ: wavelength
Δφ: phase difference
The Attempt at a...
Two different waves are starting froms points A,B respectively and going to a point C such that
$$AC - BC = 2\lambda$$
which corresponds to a phase difference of 4π
AC is given 7λ and BC is given 5λ
Now the second wave(BC) would need to have an initial phase of 4π so that the two waves can...
Homework Statement
Two waves travel next to each other for 100cm.
Wave A passes through a glass container containing liquid. The thickness of the glass in total is 1cm and the width of the liquid is 10cm. The glass has n = 1.52 and the liquid has n=1.33.
Wave B passes through a vacuum and...
what is the definition of phase lag and phase difference in waves and how are these 2 related?please explain in simple words and with real life examples.
Please explain phase,phase lag and phase difference from scratch.
One condition for wave interference is that the sources of the waves must be coherent, which means they emit identical waves with a constant phase difference.
I can understand that identical waves means they have the same wavelength. However, I don't understand what is a constant phase...
how to calculate phase difference for spherical waves?how to say whether they are in phase or out of phase?
in sinusoidal we can easily say whether they are in phase or out of phase just by looking at it,but how to do the same for spherical waves?
what is phase difference and how to visualize it?
i can understand it pretty well for sinusoidal waves,but how to visualize it for other type of waves like spherical waves,plane waves etc?
Homework Statement
There is a spring with 2 masses with a combined mass of 0.69kg. The vertical oscillation has a frequency of 1.5Hz. The amplitude of the oscillation is 30mm.
Now this spring is attached to a horizontal support rod that can be made to oscillate vertically.
how do i work out...
Homework Statement
So, my teacher said that the biggest phase difference is pi. But what if you have two waves arriving at a point, such that the instruction from one wave is a phase of (7pi/4), and from the other is (3pi/4), then the phase difference is (9pi/8), which is larger than pi. So...
Q6c)
Why is the phase difference between two points in a stationary wave equals to zero?
I understand that a stationary wave is formed by two progressive waves which have the same amplitude, frequency, wavelength and speed, but traveling in opposite directions.
Homework Statement
Light with wavelength 100nm is incident perpendicularly from air on a film 0.500μm thick
and with refractive index 2.5. Part of the light is reflected from the first surface of the film,
and part enters the film and is reflected back at the second surface, where the film is...
1. The figure shows two point sources S1 and S2 that emit sound of wavelength λ = 1.8 m. The emissions are isotropic and in phase, and the separation between the sources is d = 18.0 m. At any point P on the x axis, the wave from S1 and the wave from S2 interfere. Start with P very far away (x =...
Homework Statement
A mass-spring system with a natural frequency of 3.6 Hz is started in motion with an initial displacement from equilibrium of 6.1 cm and an initial velocity of 0.7 m/s. What is the value of ϕ?
(Question aside: Finding the amplitude of the resulting function?)
Homework...
Homework Statement
The circuit above has a 29 resistor and a 11.1 mH inductor. Calculate the theoretical phase difference between the current CPA and voltage VPB if the circuit is driven by a sinusoidal voltage source with a peak amplitude of 3.5 V at the following frequencies:
20 Hz
420 Hz...
Today, I made the following question at Physics SE, but the community redirected me here
In short, I have made a proof for EF/MF phase difference near an oscilating dipole that "vanishes" far away from the dipole. So, what I am asking for is a proof verification.
The physics SE post...