What is Superposition of waves: Definition and 24 Discussions
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 that if input A produces response X and input B produces response Y then input (A + B) produces response (X + Y).
A function
F
(
x
)
{\displaystyle F(x)}
that satisfies the superposition principle is called a linear function. Superposition can be defined by two simpler properties: additivity
and homogeneity
for scalar a.
This principle has many applications in physics and engineering because many physical systems can be modeled as linear systems. For example, a beam can be modeled as a linear system where the input stimulus is the load on the beam and the output response is the deflection of the beam. The importance of linear systems is that they are easier to analyze mathematically; there is a large body of mathematical techniques, frequency domain linear transform methods such as Fourier and Laplace transforms, and linear operator theory, that are applicable. Because physical systems are generally only approximately linear, the superposition principle is only an approximation of the true physical behavior.
The superposition principle applies to any linear system, including algebraic equations, linear differential equations, and systems of equations of those forms. The stimuli and responses could be numbers, functions, vectors, vector fields, time-varying signals, or any other object that satisfies certain axioms. Note that when vectors or vector fields are involved, a superposition is interpreted as a vector sum. If the superposition holds, then it automatically also holds for all linear operations applied on these functions (due to definition), such as gradients, differentials or integrals (if they exist).
Hello everyone, sorry if this is the wrong section. In this forum I'm a fish out of the bowl, my knowledge of physics is ages beyond most of the people on there, so please forgive my naivness.
So, here's my problem, I'm a sort of "audio" engineer (won't enter much on detail) and on my free...
All of my speculation is based on my current understanding of quantum physics as an art high school student who just has this as an interest, which is in no way at a quantum physicist's level so I apologize if this question is stupid. Also sorry for my English.
Most, if not all of you reading...
We assume incident waves to be:
y(1)=y(o)sin(wt)
y(2)=3y(o)sin(wt+Φ)
As Intensity~(Amplitude)^2
We get y(2)=3y(1)
This gives us I(2)=9I(1)
We assume I(1)=I(o) & I(2)=9I(o)
Resultant Wave Intensity I=I(1)+I(2) +2√(I(1)*I(2))*cosΦ ---->
I(o) + 9I(o) + 6I(o)cosΦ (We can take cos of this...
To answer (a), i imagineed the oscillations parallels (say to z), so we simply add ξ1+ξ2
for b, i imagined two vectors ortogonais, representing the oscillations, so we should add √(ξ1² + ξ2²), is this right?
Homework Statement
Two waves are produced simultaneously on a string of length L = 1 m. One wave has a wavelength λ of 0.5 m. The other wave has a wavelength λ of 0.2 m. The amplitudes of the waves are the same.
At t=0, at what locations x0 is the displacement y(x0) equal to zero? At what...
Homework Statement
when a point is intefered by 2 waves of different phase , the resultant is y1 + y2 ... but why the resultant amplitude can't be = A1 + A2 ... but is sqrt root ((A1)^2 + (A2)^2) ??
this is actually a online note.
Homework Equations
The Attempt at a Solution
Homework Statement
While analyzing superposition of waves from two coherent sources ,the displacement from the two sources are written as y1=A1cos(kx-ωt) and y2=A2cos(kx-ωt+∅) .The resultant displacement at any point is given by y=y1+y2 .
I am having doubt that why does argument of sine in...
Hi Guys,
I wonder if someone could help check something for me in order to make sure that I'm not making a stupid mistake with this problem as I've been marked wrong on an undergraduate paper, but I'm almost certain that I'm right. I don't quite have enough courage in my convictions to...
Homework Statement
Consider a situation in which a wave is traveling in the negative x-direction encounters a barrier and is reflected. Assume an ideal situation in which none of the energy is lost on reflection nor absorbed by the transmitting medium. This permits us to write both waves with...
Homework Statement
Secret Agent Jane Pond must retrieve the secret plans of her arch-nemesis EvilToes. These plans were tossed (by one of EvilToes’ bumbling henchmen) down a well of unknown depth. Jane is carrying a rope 10m long and a “standard issue VPG-C1C7”. (The VPG-C1C7 is a device...
Homework Statement
Find the combined elongation of the waves 7sin(wt) and 2sin(wt + pi/4). Express it both in real and complex form.
Homework Equations
A = sqrt(A12 + A22 + A1A2cos(Δθ)
The Attempt at a Solution
I was given the formula above, which I don't understand, but it does...
Homework Statement
Using expansion of sin and cos functions, show that the resultant of adding the following two waves:
a) E1 = E01*sin(wt-k(x+Δx))
b) E2 = E01*sin(wt-kx)
Gives: E = 2E01*cos((1/2)kΔx)*sin[wt-k(x+Δx/2)]
Homework Equations
N/AThe Attempt at a Solution
I don't know how to sum...
hi...
Got to ask about superpostion of waves...
When two coherent light waves cross each at some point in space moving in different directions, do they superimpose?
If they do, do we need a screen to be able to see the resultant or we can see it directly.
Let's just assume we have a laser...
Homework Statement
Consider the superposition of two waves;
\zeta_1 + \zeta_2 = \zeta_{01} e^{i(kr_1 - wt)} + \zeta_{02} e^{i(kr_2 - wt + ∅)}
where ∅ is a phase difference that varies randomly with time. Show that the time-averages satisfy;
<|\zeta_1 + \zeta_2|^2> = <|\zeta_1|^2> +...
Homework Statement
If sound waves superimpose, why is a person in the audience able to distinguish different sources of sound eg flute and guitar.
Homework Equations
Amplitude (A+B) = Amplitude (A) + Amplitude (B)
The Attempt at a Solution
No idea
Intensity and Superposition of waves...
Homework Statement
Incident wave y=Asin(ax + bt + pi/2) is reflected by an obstacle at x=0 which reudces intensity of reflected wave by 36%. Due to superposition a resulting wave consist of standing wave and traveling wave given by y= -1.6 sinax.sinbt +...
I am trying read through a chapter on properties of matter waves in Eisberg & Resnick's Quantum Physics. In section 3-4, a superposition Ψ of 7 sinusoidal waves, each with a different reciprical wavelength and amplitude, is shown along with all the component waves(fig. 3-9). He defines the...
Figure on top:
P_{1}= (1/16)W, P_{2}=1W, P_{3}= 16W, and I want to calculate how the intensity varies with \theta
y(r,t) = y_{2}(r,t)[1 + 4e^{i(\phi_{3} - \phi_{2} + kdsin \theta} + \frac{1}{4} e^{i(\phi_{1} - \phi_{2} - kd sin \theta)}]
I understand how to proceed here, I just want to...
Hey everyone, I've just stumbled across this forum on Google while trying to find something to help me understand a question.
I've just started studying physics at AS level at sixth form, and I've been given this piece of homework, with the teacher not explaining it too well, so, I'm stuck...
Homework Statement
Learning Goal: To see how two traveling waves of the same frequency create a standing wave.
Consider a traveling wave described by the formula
y_1(x,t) = A \sin(k x - \omega t).
This function might represent the lateral displacement of a string, a local electric...
Homework Statement
2. The attempt at a solution
i knew how to solve questions one and three..please help me in question number 2...here is what i did...
Question 1
(2*pi*x)/(wavelength)=pi/3
where x is the distance between the two waves (5cm)
and therefore we get the...
hi..
Juz want to know if 2 waves were to interfere each other, in order to find the max intensity, is it possible to juz add the 2 wave intensity to find the max? if given that wave 1 intensity is
For a superposition of two since waves of equal amplitude in a dispersive media, we find that the group velocity is given exactly by
v_g = \frac{\omega_2-\omega_1}{k_2-k_1}
and approximately by d\omega / dk|_{k=k_0}.
How do we show that this approximation holds for any type of waves...