What is Amplitudes: Definition and 108 Discussions
The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). There are various definitions of amplitude (see below), which are all functions of the magnitude of the differences between the variable's extreme values. In older texts, the phase of a period function is sometimes called the amplitude.
For this,
The two statements highlighted do not seem to agree. I think the first statement highlighted is referring to A as initial amplitude (which we can denote ##A_i##) of the traveling waves before there constructive interference to form antinodes with an amplitude 2A and nodes of an...
The trig identities for adding trig functions can be seen:
But here the amplitudes are identical (i.e. A = 1). However, what do I do if I have two arbitrary, real amplitudes for each term? How would the identity change?
Analysis: If the amplitudes do show up on the RHS, we would expect them...
I have attempted the question using the large formula here with figures from the waveform with n as 3 & 101:
however I think that the large formula is for the total waveform encompassing all harmonics as the 3rd and 101st harmonic amplitudes are very similar 10.9662222 *10^-6V for the 3rd...
If I consider the MWI, one of the notions for what happens during measurement is that the initial wavefunction, if I use Dirac notation and two dimensions, ##|A\rangle+|B\rangle## undergoes the transformation ##(|A\rangle+|B\rangle)|E_{before}\rangle \rightarrow...
I am a graduate student with a somewhat basic level of exposure to qft. As part of my degree I have been tasked with calculating meson decay amplitudes in a paper provided to me by my supervisor but unfortunately I seem to be lacking some prior knowledge to understand why certain expressions are...
Before I start, let me say that I have looked into textbooks and I know this is a standard problem, but I just can't get the result right...
My attempt goes as follows:
We notice that the amplitude of this diagram is given by $$\begin{align*}K_2(p) &= \frac{i(-i...
Playing 440 Hz, what are the approximate harmonic amplitudes for a trumpet? For a flute?
This is to help students understand the differences when those instruments play the same note.
I've been to many website, including University of New South Wales. I would like the frequency spectrum in...
I know $$ i\mathcal{M}(\vec {k_1}\vec{k_2}\rightarrow \vec{p_1}\vec{p_2})(2\pi)^4\delta^{(4)}(p_1 +p_2-k_1-k_2) $$ =sum of all (all connected and amputated Feynman diagrams), but what is meant by 1 loop order? In other words, when I take the scattering matix element...
I'm coming back to physics after a long so apologies if this has a basic answer- How can the amplitude of a longitudinal sound wave be increased without increasing its wavelength? I understand what it would look like graphically if a low amplitude sine wave and high amplitude sine wave were...
This is QFT for the gifted amateur, chapter 19, which is generating the various Feynman diagrams and rules. Some calculations are given but I encounter various problems when trying to work them all out.
The starting point is that we want to calculate:
$$\langle q| \hat S | p \rangle = (2\pi)^3...
I was studying the photon polarization sum process (second edition QFT Mandl & Shaw,https://ia800108.us.archive.org/32/items/FranzMandlGrahamShawQuantumFieldTheoryWiley2010/Franz%20Mandl%2C%20Graham%20Shaw-Quantum%20Field%20Theory-Wiley%20%282010%29.pdf) and got stuck in how to get certain...
I am not sure what I can do with the equation. I realize that ## \vert c_1 \vert ^2 = \vert c_2 \vert ^2 = \frac{1}{2} ## does not mean that ## c_1 ^2 = c_2 ^2 = \frac{1}{2} ## or that ## c_1 = c_2 ##, so I don't know how to use it. I think ideally I might have something like ##P = \vert c_1...
If anyone is familiar with the calculation of scattering amplitudes using momentum twistors. I am working through the book "Scattering Amplitudes in Gauge Theory and Gravity" by Elvang and Huang.
I am completely stumped by one step that should be simple. My question is about Eq. (5.45). My...
So, my game is coming along.
My psychic energy shielding protects against EM radiation. The energy used for shielding gets depleted based on the type of EM radiation (the wavelength) and according to the amplitude of the radiation the energy shielding is exposed to.
I can't find many numbers...
I understand that the Fourier transform is changing the domain (time/space) to frequency domain and provides the sin waves. I have seen the visualizations of Fourier transform and they are all showing the transform results as the list of frequencies and their amplitude. My question is, what if...
Hi there,
While reviewing the theory of Feynman diagrams for QED, a question came into my mind. In the textbooks, one usually deals with processes involving two incoming particles. But I could imagine a process where four particles are interacting (e.g. attached picture) and this can give a...
Hi All,
I would like to know who was the first scientist to use probability amplitudes in solving either math or physics problems.
Best wishes,
DaTario
Hello! In Schwarz's QFT he introduces in chapter 27 the Spin-Helicity formalism as a way of calculating gluon-gluon interactions much easier than going through all the Feynman calculus from the beginning to the end. It seems so amazing, but I am not sure I understand what is the fundamental...
Hi all, I am rather confused about the following concept. Assistance is greatly appreciated!
A time-dependent probability amplitude can be written as
$$\langle a_k| e^{-\frac{i}{\hbar}\hat{H}t} |\psi\rangle$$
where ##a_k## is an eigenvalue. Suppose I want the x-representation of the ket, I can...
I’m currently self-studying from Feynman & Hibbs Quantum Mechanics and Path Integrals, but having trouble with a statement in the chapter on time-dependent perturbations.
Background: They define
$$V_{mn}(t_c) = \int_{-\infty}^\infty \phi_m^*(x_c)V(x_c,t_c)\phi_n(x_c)\,dx_c,$$
where V(x,t) is...
Is A_pp(s,t)=A_pBARp(t,s) true based on crossing symmetry?
Consider pp and pBARp elastic colissions (p + p -> p + p and p + BAR(p) -> p + BAR(p)). The scattering amplitudes are related by crossing in the following way:
1) A_pp(s,t)=A_pBARp(u,t) \simeq A_pBARp(-s-t,t) (energy large compared to...
Homework Statement
Show that the ratio of two successive maxima in the displacement of a damped harmonic oscillator is constant.(Note: The maxima do not occur at the points of contact of the displacement curve with the curve Aeˆ(-yt) where y is supposed to be gamma.
2. Homework Equations The...
In reading about the photoelectric effect I noted that frequency accounts for the energy of the photon which must be high enough to liberate free electrons and the amplitude is the cause of intensity.Now, how can the amplitude be responsible for more than the liberation of more than one photon...
Hello,
I am having a hard time understanding a result relating to a michelson interferometer. I always assumed that when the beam hits the wave splitter both resulting waves will have half the amplitude of the original wave. However using this assumption does not give the correct irradiance for...
I suppose the answer is no, since there is no reason to believe that it does. Or is there any? Has this been tested experimentally? Or is there an obvious reason that it does or does not?
Here's a picture that was in my textbook - they are the patterns of interference and diffraction of a light wave. I don't get why the interference amplitudes are all equal. Aren't they supposed to be higher in the middle and lower as they move away from the center??
after substituting in your omega, can you multiply a transfer function by an input signal's amplitude, and expect the result to be the amplitude of the output? (once converted to polar)
This might be a shortcut way to find your amplitude when you don't really need a representation of the whole...
In classical mechanics and EM, the energy carried by a wave is the amplitude squared. In QM the (complex) amplitude squared of the position-space wave function is the position probability density. Do physicists regard this as anything more than just an interesting coincidence? Has anybody...
I have been reading about QFT amplitudes. It seems that difficulty increases as we consider more and more terms in the Dyson's expansion for the Scattering operator, and we need to normalize each of them if we want to get a sensible result.
My question is, nature usually uses what order? I...
I think the story where abelian, i.e. U(1), gauge symmetry comes from is pretty straight-forward:
We describe massless spin 1 particles, which have only two physical degrees of freedom, with a spin 1 field, which is represented by a four-vector. This four-vector has 4 entries and therefore too...
Homework Statement
This isn't homework, but rather a task I have to solve at work. I am a bit lost and don't know where to start and would like some hints on how to make this an automated calculation in MATLAB.
I have an area, let say a square that is rotated 45 degree (this can change in...
Homework Statement
What are the associated peak amplitudes of the E and H fields if sunlight has a maximum intensity of 1400 W/m2 on the earth’s moon?
Homework Equations
I = <s> = 1/2 c ε0E2The Attempt at a Solution
I = <s> = 1/2 c ε0E02
1400 = (1/2)(3*108)(8.85*10-12)(E02)
1400 /...
When discussing about generalized coordinates, Goldstein says the following:
"All sorts of quantities may be impressed to serve as generalized coordinates. Thus, the amplitudes in a Fourier expansion of vector(rj) may be used as generalized coordinates, or we may find it convenient to employ...
According to the old thery of light the energy carried by by a wave is proportional to the amplitude of the electric field not to the frequency as Planck proposed, so an eletromagnetic radiation in the gamma spectrum carry the same energy as a radio one if their amplitude is the same?
They only...
Would there be destructive interference if I had two waves that are superimposed and the peak of one wave met the trough of the other but they both have different amplitudes? If there isn't total destructive interference, then what does the final wave look like?
Hi all,
I've recently been reading a paper by Richard Muller and Shaun Maguire (which is not the exact topic of this post). In that work, the authors mention:
"We note that in quantum field theory, very small, localized and rapid events contain amplitudes that can be interpreted as taking...
Homework Statement
In the automotive damper test machine mentioned in Task 1 the damper is mounted vertically, the top end connected to a static fixing, the bottom to a table which is moved vertically by an actuator. The moving mass is 500kg, and the design case for the rig is based upon...
Hi everyone, with this thread I kindly seek for advice from more experienced people to hear as many opinions as possible. I will try to explain the situation clearly:
I am doing a 4 years Msci programme in Theoretical Physics, in which I almost completed the third year. During the third year...
Hello everyone! I am in a pickle right now as I attempt to move forward in my research project on neurofeedback. I am trying to calculate the theta/beta ratio for individual subjects and then compare them statistically. The issue I am having is statistically comparing amplitudes of different...
Hi All,
Was there any use of the concept of amplitudes of probability before their use in quantum mechanics?
In connection to this question, who invented or was the first to use this resource?
Best wishes,
DaTario
Homework Statement
I'm looking at an E&M textbook - "Time-Harmonic Electromagnetic Fields". They state:
"A more general ##x ## polarized field is one consisting of waves traveling in opposite directions with unequal amplitudes - i.e :
(1) $$ E_{x} = Ae^{-jkz} +Ce^{jkz}$$
Let ## A ## and...
Note from mfb: I fixed the LaTeX formulas
http://image.keyan.cc/data/bcs/2015/0428/w84h1446064_1430226899_628.jpg
I met some trouble by using latex on this version, so I try to add the image from the pdf,
the Latex code is as follow if any help.
The lowest order lagrangian for ChPT is...
So this is basic question but the more I read the more I am confusing myself!
I was assuming that the wavelength of a photon was the same wavelength as the associated probability amplitude (although a complex number). So to make constructive interference it means one path takes say ten...
Note: I'm posting this in the Quantum Physics forum since it doesn't really apply to HEP or particle physics (just scalar QFT). Hopefully this is the right forum.
In Peskin and Schroeder, one reaches the following equation for the spacetime Klein-Gordon field:
$$\phi(x,t)=\int...
Homework Statement
During one complete cycle, a wave moves through ___ wavelength, ___ period, __ amplitudes
Homework EquationsThe Attempt at a Solution
Well I got 1 wavelength, 1 period, and 2 amplitudes
But apparently the answer is 1 wavelength, 1 period, and 4 amplitudes
But I don't see...
Homework Statement
By what factor does the amplitude decay in the time interval (which I had to find).
E: stored energy
γ:damping rate
a: amplitude
t: time
Q: quality factor
T:Period
ω: frequency
Homework Equations
Q = 2∏E/(ΔE)
The Attempt at a Solution
I found the interval to be t=QT
but...
1. If there is a sound wave traveling in the air, will the amount of air transported by the wave be proportional to the intensity of the wave?
Here is my answer: yes, because as the energy of the wave is related to the square of the amplitude of oscillations, the more energy you have, the more...
Homework Statement
A point mass M is concentrated at a point on a string of characteristic impedance ρc. A transverse wave of frequency ω moves in the positive x-direction and is partially reflected and transmitted at the mass. The boundary conditions are that the string displacements just to...