Standing wave Definition and 201 Threads

In physics, a standing wave, also known as a stationary wave, is a wave which oscillates in time but whose peak amplitude profile does not move in space. The peak amplitude of the wave oscillations at any point in space is constant with time, and the oscillations at different points throughout the wave are in phase. The locations at which the absolute value of the amplitude is minimum are called nodes, and the locations where the absolute value of the amplitude is maximum are called antinodes.
Standing waves were first noticed by Michael Faraday in 1831. Faraday observed standing waves on the surface of a liquid in a vibrating container. Franz Melde coined the term "standing wave" (German: stehende Welle or Stehwelle) around 1860 and demonstrated the phenomenon in his classic experiment with vibrating strings.This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite directions. The most common cause of standing waves is the phenomenon of resonance, in which standing waves occur inside a resonator due to interference between waves reflected back and forth at the resonator's resonant frequency.
For waves of equal amplitude traveling in opposing directions, there is on average no net propagation of energy.

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  1. nav888

    Microwave standing wave calculations (max/min Intensity, Wavelength)

    I have tried to subtract the two values of y for the minimum intensities to find half the wavelength but I am really stuck. Any help would be appreciated thanks
  2. Spinnor

    I Let a standing wave of length L go, get traveling wave of length 2L?

    Consider a very long string between fixed supports of mass density rho and tension T. At a distance 1 meter from one support pinch the string. The pinching does not change the tension. Adjust the mass density or tension so that when we add energy to this section of string we produce the first...
  3. maxelcat

    Standing wave, phase and antiphase

    I think I understand that points P and R are pi radians out of phase - reaching their max/min at the same time. But are P and Q in anti phase? What is antiphase exactly - is it when they are 180deg out of phase - or is it when they are anything other than totally in phase? I seem to find...
  4. A

    Travelling wave and standing wave

    I wasn't sure about my solution for part c. I said "same distance as for traveling wave ie \lambda/2=0.06m". Also how do you enter LaTeX on this forum?
  5. V

    Reflection of sound wave in an open organ pipe

    I know that standing waves form in an open organ pipe. Since, standing waves can only form from superposition of original wave and reflected wave, so there must be a reflected wave in an open organ pipe. But I fail to understand how sound wave can reflect at the open end of organ pipe.
  6. S

    Amplitude of standing wave for higher frequency

    I understand the part where there will be more nodes produced because number of wave produced will increase (let say from half wave to one wave). But I don't understand the part where the amplitude will be less. How can number of nodes (or frequency) affect the amplitude of standing wave...
  7. V

    B Potential energy in standing wave compared to traveling wave

    From hyperphysics, "The unique point in the case of the traveling wave in the string is the element of the string that is at the maximum displacement as the wave passes. That element has a zero instantaneous velocity perpendicular to the straight string configuration, and as the wave goes "over...
  8. bubble-flow

    Where are the pressure nodes on a standing acoustic wave in water?

    I have calculated the wave length of a 36 kHz acoustic wave in 20 °C water to be around 41.16mm. Suppose I have a transducer that produces a 36 kHz acoustic wave and a small water container with a length of 41.6 mm. How will the standing acoustic wave look like, which is produced by the...
  9. P

    I How does a standing wave form?

    I understand how waves undergo superposition. However, for a standing wave, the reflected wave is a mirror opposite of the incoming wave. By the superposition principle, won’t the 2 waves add up to 0, at all points?
  10. B

    Solving the wave equation for standing wave normal modes

    ## \frac {\partial^2 \psi} {\partial t^2} = v^2 \frac {\partial^2 \psi} {\partial x^2} ## has solution ## \psi (x, t) = \sum_{m=0}^\infty A_m \sin(k_mx + \alpha_m)sin(\omegat + \beta_m) ## The boundary conditions I can discern $$ \psi (0, t) = 0 $$ $$ \frac {\partial \psi} {\partial x} (L, t)...
  11. maxelcat

    Maximizing Profit in Online Business

    Here's my working. Perhaps I make some wrong assumptions?
  12. A

    I Can the energy in two waves cancel out? If so, why?

    I know the answer would be yes, but why? In class, I learned that energy is scalar and cannot be negative (at least in undergraduate class). Thus adding two sources of energy should result in a higher level of energy in general. But here for wave, if we have 2 waves that do destructive...
  13. N

    Optics homework: Why is this equation called a standing wave?

    ψ(y,t)= -2A sinky sin wt Why is this called a standing wave?
  14. H

    Exploring the Phenomenon of Longitudinal Standing Waves

  15. Vivek98phyboy

    Reflection of inverted waves to form a standing wave

    Standing waves in a string fixed at one end is formed by incoming and reflected waves. If reflected waves are 180° out of phase with incoming wave, how could they combine to give an oscillating wave? Shouldn't it be completely destructive interference all the time across the whole length of string?
  16. P

    B Animation of a standing wave formed by components from a free end

    This is not a homework question, it is for my understanding so please do not answer this question with a question. I have found this great animated gif but it appears to be for a fixed end (notice wave inversions at the end). Has anyone seen a similar one for a free end? Many Thanks
  17. E

    Minimum frequency for a point to have maximum amplitude in standing wave

    When I tried using the equations the only thing I could see is that it is impossible for such point to be an anti-node. In this case, how do I find the frequency? The answer is not even with the form of v*n/2L which is very confusing to me, I thought that the frequency of a standing wave must...
  18. Fdtroya

    Node Counting Circuit for Standing Wave Generator

    Summary: Make a circuit that counts the number of nodes in a standing wave generator I have a an assignment to complete this Term, the assignment consist in making a machine that would produce standing waves in various frequencies, (for example the typical motor connect to a string with...
  19. P

    A Real image of a sawtooth standing wave in a musical string?

    Hi there I am teaching resonance and standing waves in stringed instruments at the moment at high school. The theory states that a number of standing waves simultaneously (harmonics) exist in a naturally vibrating musical string, but with varying amplitudes, the 1 st harmonic being loudest...
  20. Nikhil Rajagopalan

    Standing Wave Fundamental Frequency and Particle Vibration

    For a wave A sin ( kx - ωt) and a wave A sin ( kx + ωt) traveling opposite to each other, on evaluating by applying superposition principle , the resultant displacement function is 2A sin ( kx ) cos (ωt) . For different Node Anti-node configurations we calculate natural frequencies of the...
  21. Arman777

    How Do You Calculate the Energy of a Standing Wave?

    Homework Statement Derive the energy of the standing wave. Homework Equations Standing wave equation: $$y(x,t)=2Asin(kx)cos(ωt)$$ The Attempt at a Solution I am trying to derive the energy of the standing wave. But I am kind of stuck at the approach. Standing wave has no translational...
  22. D

    Standing wave transverse motion and amplitude

    Homework Statement A guitar string is vibrating in its fundamental mode, with nodes at each end. The length of the segment of the string that is free to vibrate is 0.381m. The maximum transverse acceleration of a point at the middle of the segment is 8600 m/s and the max. transverse velocity is...
  23. A

    Which Frequency is NOT Possible for a Vibrating String?

    Homework Statement A string (m = 1 kg) fixed at both ends is vibrating in its second harmonic mode. If the length of the string is 2 m and it feels 50 N of tension, which of the following is NOT a possible harmonic frequency for this string? a) 1.25 Hz b) 2.5 Hz c) 5 Hz d) 10 Hz e) 20 Hz...
  24. H

    New wave after superposition (interference)

    Homework Statement 1. Homework Statement [/B] The displacement y of standing wave that is obtained by a superposition of waves : Y1 = 3 sin (2##\pi##(0.5t - 0 25 x)) Y2 = 3 sin (2##\pi##(0.5t + 0 25 x))Homework Equations Formula for standing waves Y = 2Asinkx coswt The Attempt at a Solution Y1...
  25. Ari

    Frequency of a standing wave based on slope?

    <Moderator's note: Moved from a technical forum and thus no template.> I've done an experiment on standing waves on a string. By graphing √T vs λ (where T is tension and λ is wavelength) using the linearized equation √T = (1/√μ) f ⋅ λ, I was able to get this data: μ = .000256 kg/m slope = 1.78...
  26. R

    I Clarification for a standing wave on a string equation

    Hello, Came across https://drive.google.com/file/d/1bpB7BcVf1yQLiwg9quAn2vlhu8-i6Zy_/view and I'm not sure about one thing For the 2 parts of the equation with sin, is it: 1. [...sin(kx)]sin(wt) or is it: 2. [...sin(k)*x]sin(w)*t Thank you -DR
  27. D

    Tension and frequency of a vibrating violin string

    1. The problem statement, all variables, and given/known data So I'm doing an IB extended essay on the relationship between frequency and tension of a violin string. As you apply more tension to the string (using weights and pulley), the frequency will be higher, as shown below. There's not too...
  28. S

    Y-intercept of a lambda square VS tension of standing wave

    Hi all! I am doing an experiment where we create a standing wave by attaching a string to a hanging mass at one end and to a string vibrator at the other (the string passes through a pulley). When plotting the graph, the slope is inevitably 1/(u*f^2) where u is the linear density and f the...
  29. EF17xx

    Tuning fork standing wave in a water pipe

    Homework Statement The question is as follows: The distance between the two positions of maximum loudness is x What is the wavelength of the sound emitted by the tuning fork ? A. x/2 B. x C. 3x/2 D. 2x the correct answer is answer D. Homework Equations Pipe with two ends open λn=...
  30. EF17xx

    Standing wave in a tube -- multiple choice question

    Homework Statement The correct answer according to answer sheet is answer B. Homework Equations λn= 2L/n (both ends open) λn = 4L/n (one end open one end closed) c=λf Speed of sound does not change. as it is still in air... (correct assumption? ) The Attempt at a Solution f1= 500Hz L =...
  31. R

    Error calculation for µ in standing wave experiment

    Homework Statement I experimented with standing waves on an oscillating string, and I was asked to calculate the absolute error of µ (linear mass per unit length). I don't know how to calculate it, so please help me. I loaded 100g, 200g and 300g on the string. Below are tabulated data of the...
  32. Z

    Calculating Mass of a Vibrating String Using Known Quantities

    Homework Statement A second harmonic standing wave has the known quantities of Amplitude (max y at antinode) A, maximum velocity (y=0 at antinode) v, string length L, tension in the string T. Given that we know that it is second harmonic, we can assume that λ = L How can one determine the...
  33. EF17xx

    The Resonating Wineglass Problem: Understanding the Equation and Variables

    I have done an experiment where I vary the levels of water in a wineglass and record the frequencies it produces which differ depending on the height of the water. Below you see 1 equation, apparently I can use this equation to mathematically prove my results from my experiment, (this equation...
  34. T

    Relationship between standing wave and resonance?

    <Moderator's note: Template removed due to replacement in a technical forum.> In the textbook, it said that standing waves only occur at the resonant frequencies of the medium. I don't understand why. My understanding of standing waves is that it is when the medium length (slinky) is a...
  35. SchroedingersLion

    A Enhancing Spontaneous emission in a vacuum standing wave

    Hi, it is well known that spontaneous emission of an atom can be enhanced, if the atom sits at a node of the vacuum standing wave field in a cavity. My question is, why is it the node? At a node of a standing wave, there is zero intensity, so there should be no interaction between the atom and...
  36. E

    I Will Increasing Tension of a Two Loop Standing Wave Change its Frequency?

    Hello all, I am doing this question where it asks if I increase the tension of a two loop standing wave without changing the frequency, what kind of standing wave will I get? I came to the conclusion that it would become a one loop standing wave as f= 2L/(n) as I plugged in 2 for n and I got...
  37. T

    I Transmission in Single Mode Waveguide

    Hello there, I was wondering if the power profile of a single mode waveguide can be changed? I mean, a wave that travels through the waveguide will have a harmonic shape, right? Is it possible to get a different shape of the power profile? Thank you :)
  38. L

    Resonance box with tuning fork, standing wave

    Homework Statement There is a resonance box with one end cloesd and the other end open. The box reinforces the sound of the tuning fork. That sound has frequency of 440 Hz sound velocity is 340 m/s a.) What is the basis of the phenomenon in question? b.) define the shortest possible length of...
  39. Const@ntine

    Finding Nodes in a Standing Wave at 800 Hz

    Homework Statement Two identical loudspeakers are driven in phase by a common oscillator at 800 Hz and face each other at a distance of 1.25 m. Locate the points along the line joining the two speakers where relative minima of sound pressure amplitude would be expected. Homework Equations v...
  40. Basov

    A How a laser resonator generates the standing wave?

    Hi, guys. I'm interrest in the question about how optical (laser) resonator can generates the standing wave? As i know, there is a condition that the resonator base (lenght between two mirrors) should be multiple to the length of the wave. (L=k*(lamda/2)). But in practice no one never measures...
  41. L

    Find two lowest frequencies standing wave

    Homework Statement A metal bar is attached into a vice in the middle. Bar is hit with a hammer creating a longitudinal standing wave find the two lowest frequencies. Bar's length l= 3m wave velocity = 5100m/s Homework Equations wave equation ## v = \lambda * f ## The Attempt at a Solution...
  42. T

    Traveling and Standing Wave Equations

    Homework Statement I am really confused with the equations. For traveling waves, in some places they write y = A cos (kx - wt) for waves traveling in the positive x-direction. Then some write y = A sin (wt - kx) for waves traveling in the positive x-direction while others write y = - A sin (wt...
  43. Phil Freihofner

    I Standing wave in cylindar vs cone

    I have been trying to understand why two woodwind bore shapes behave so differently. My understanding is that one end of a woodwind is an antinode (driven by the reed of the instrument) and the other end is a node (where the tube is open to the atmosphere). a - - - - - - - - - - n In the...
  44. K

    I Bohr model, Why do we assume a standing wave?

    Hi, I wonder why we assume the matter wave of an electron is standing wave. Is there any reason why it has to be standing wave?Is it because standing wave is the right "wave equation solution" that satisfies integer multiple behaviour of bohr model?
  45. S

    B Moving to a higher harmonic in a standing wave

    Imagine that you have plucked a string and it is vibrating as a standing wave at its fundamental tone (frequency f1). You leave it there and later on come back with the intention of bringing it up to the second tone (frequency f2). What should you do? It seems obvious: apply a stimulous...
  46. K

    I About creating standing wave with laser

    Hi all, I remember the standing wave is introduced in a chapter of mechanical wave in my undergraduate physics times ago. It is said that two waves of the same frequency propagating the opposite directions will form a standing wave in space. I wonder if it is possible to produce the standing...
  47. pliep2000

    I State space of a standing wave?

    Lets say a state is defined by the minimal amount of independent variables to completely describe a system. One would come up with the (q,p)-phase-space for a point mass and as another example the Hilbert-space for quantum-states. Consider the very simple case of a standing wave in string...
  48. T

    Standing wave in a column of methane, find gamma of methane

    Homework Statement A standing wave with a frequency of 1100 Hz in a column of methane at produces nodes that are 0.200 m apart. What is the value of γ for methane? (The molar mass of methane is 16.0 g/mol)Homework Equations v = sqrt ( γRT/M) where R is 8.341, T = 20 °C and M = 16.0 g/mol. v=fλ...
  49. C

    Pressure standing wave nodes at the end of the open side of

    I do not understand why standing sound waves can be formed in a one-side or two-side open tube. Consider a one-side open tube. In particular how does the reflection of the wave at the open end occur? I found the following explanation. I do not get why the pressure at the open end cannot vary...
  50. i_hate_math

    Standing Wave Period for Third Harmonic Oscillation

    Homework Statement A rope, under a tension of 209 N and fixed at both ends, oscillates in a second-harmonic standing wave pattern. The displacement of the rope is given by y=0.49sin(πx/3)sin(12πt) What are (a) the length of the rope, (b) the speed of the waves on the rope, and (c)the mass of...
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