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


{\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).

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  1. I

    I Approach to extrapolate a "superpositioned" wave?

    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...
  2. E

    B Question about quantum superposition

    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...
  3. warhammer

    Intensity Distribution of Superposition of 2 Waves

    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...
  4. LCSphysicist

    How do we combine two waves to create Lissajous figures?

    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?
  5. TheDemx27

    Find the Maximum of Superposition of Waves

    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...
  6. D

    Why Is the Resultant Amplitude of Interfering Waves Not Simply A1 + A2?

    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
  7. T

    Simple doubt in superposition of waves

    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...
  8. A

    Superposition of waves - constructive or destructive interfernce?

    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...
  9. G

    Superposition of Waves - Standing Waves

    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...
  10. S

    Can Secret Agent Jane Pond Retrieve the Plans at the Bottom of the Well?

    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...
  11. G

    Superposition of waves formula

    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...
  12. heycoa

    Optics, Superposition of waves

    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...
  13. A

    Superposition of waves, result visible?

    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...
  14. S

    Time-averages of superposition of waves.

    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> +...
  15. P

    Understanding Source Differentiation in Sound Wave Superposition

    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
  16. A

    Intensity and Superposition of waves

    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 +...
  17. T

    Δκ of a superposition of waves

    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...
  18. L

    Calculating Intensity Variation in Superposition of Waves

    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...
  19. S

    Superposition of Waves - Please help

    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...
  20. D

    Superposition of waves as a product of y(x) and y(t)

    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...
  21. B

    How Do I Find the Distance Between Two Waves in Superposition?

    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...
  22. P

    Can Two Interfering Waves' Intensities Simply Be Added for Maximum Intensity?

    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
  23. H

    Analyzing Superposition of Waves with Different Phases

    How do I find the sum of these 2 waves, Asin(kx-wt) and Asin(kx+wt)? I have no clue how to add 2 sins with diffent phases. Thank you for your help!
  24. quasar987

    Group velocity for a discrete superposition of waves

    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...