Standing waves Definition and 259 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. R

    What is the relationship between tension and number of loops in a standing wave?

    To demonstrate standing waves, one end of a string is attached to a tuning fork with a frequency of 120 Hz. The other end of the string passes over a pulley and is connected to a suspended mass M. The value of M is such that the standing wave pattern has four "loops". The length of the string...
  2. T

    Standing Waves with One Fixed End: Relationship Explained

    I know that typically, standing waves (liek those produced in a musical instrument sloed at both ends, or by a rope tied to a point) have a relationship between the length (of the rope/instrument) and the possible wavelengths characterized by wavelength = 2xlength / n where n is an integer...
  3. W

    What is the relationship between water height and standing waves in a tube?

    Homework Statement A 1.0--tall vertical tube is filled with 20 water. A tuning fork vibrating at 573 is held just over the top of the tube as the water is slowly drained from the bottom. At what water heights, measured from the bottom of the tube, will there be a standing wave in the tube...
  4. J

    Standing Waves: 2m, 1m, 4m, 1.5m, 67cm - Which Doesn't Fit?

    If two of the wavelengths of standing waves on a 12m rope secured at both ends are 2m and 1m, which of the following COULD NOT be a standing wave wavelength on the same rope with the same tension? 4m, 2.5m, 1.5m, or 67cm. 2L/n=lamda I said 2.5m because this does not give an...
  5. Y

    Standing waves in surface vibrations in rods?

    I appologize in advance if this problem will be awkwardly presented, but I'm a biologist, with no talent for physics or mathematics whatsoever. Here goes... At my institution, we are researching communication of certain bugs, which use low-frequency, substrate-borne vibrations as signals...
  6. T

    How Do Microwaves Create Standing Waves in an Experiment with a Movable Mirror?

    Homework Statement I have an expirement when we use microwaves to produce and observe standing waves. There is a transmitter up at A and a receiver at B. There is also a mirror which is parallel to AB and moves in a parallel motion to AB. Due to the design of this, there are 2 paths, one...
  7. S

    Understanding Energy in standing waves

    Hi all, I've been unable to understand how energy remains standing b/w nodes & antinodes.What's the behaviour of energy in nodes & antinodes.Plz. help.Thanks.
  8. N

    Standing Waves in Open Pipes: How Do Sound Waves Reflect at the Open End?

    Hi How are standing waves set up in open pipes - my book says that the sound waves can be reflected from the open end of the pipe - how is this possible - surely the wave would just leave the pipe? Thanks in advance
  9. N

    Standing waves and resonance frequency

    Homework Statement Hi all. I have shown that standing waves occur on a string of length L (fastened at x=0 and x=L) for angular frequencies: \omega_n=n\frac{v\pi}{L}. Are these frequencies the same as the strings resonance frequencies? Thanks in advance. Regards, Niles.
  10. F

    Standing waves in a funny Potential distribution

    Homework Statement The description of the potential distribution is given in the attached image. The particle arrives from the left with E>V0. write the solutions to the S.E in regions x<o and x between o and a Homework Equations I believe psi(x)= e^ikx+Re^-ikx in x<0 and...
  11. J

    Standing Waves Formula Question

    Homework Statement In the equation describing the superposition of the two waves to obtain a standing wave, which term represents the wave propagating to the left? Homework Equations Y(x,t) = Asin2\pi(t/T - x/\lambda) + Asin2\pi(t/T +x/\lambda) The Attempt at a Solution I think its...
  12. N

    Frequencies of the normal mode in standing waves in a string fixed

    hi,im a newbie over here,my physics quite poor so i really need help by understanding it,i jz wanted to ask could any1 please explain to me what is in phase,&out of phase?;im totally baffled.:blushingAnd what's frequencies of the normal mode in standing waves in a string fixed in both ends?i...
  13. D

    Why Does Bragg Reflection Cause Standing Waves?

    Homework Statement I've got my exam in solid state physics tomorrow, and although I've understood most of the most complex subjects now, I feel I'm missing the understanding on one fundamental phenomena; Bragg reflection.. Throughout Kittel it's mentioned, that when we're at the first...
  14. S

    Help with microwave oven standing waves problem

    Homework Statement Hey guys, I have a homework problem in my electromagnetism class that's got me a little stumped. I'm supposed to measure the interior dimensions of my microwave oven and use that to calculate the 5 lowest frequencies at which I can sustain a mode in which I have standing...
  15. V

    Exploring Standing Waves on a Stretched String: Wavelengths and Patterns

    Homework Statement A stretched string fixed at both ends is 2.0 meters long. What are three wavelengths that will produce waves on this string. Name at least one wavelength that would NOT produce a standing wave pattern.Homework Equations The Attempt at a Solution Since standing waves have...
  16. G

    How Are Nodes and Antinodes Located in Standing Waves Between Two Speakers?

    Two speakers 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 a line joining the two speakers where relative minima of sound pressure amplitude would be expected (Use v = 343 m/s). This problem ended up screwing my mind...
  17. G

    Matter waves as standing waves

    Hi all,can anyone tell me the meaning of lines that i had read from a book: "The electron is situated within a distance of 10 to the power -8 to 10 to the power -10 m. from the nucleus and is always confined only within this distace. The matter waves associated with electron is defined in terms...
  18. G

    Exploring Standing Waves and Their Properties

    Hi all,actually i want to discuss about standing wave. Its little bit confusing to me.As a simple defintion,when two waves of equal amplitude travel in opposite direction then what the resultant wave,for which there is no propagation of energy is called standing waves. But another...
  19. P

    What Are the Possible Frequencies of Oscillations for a Clamped String?

    Homework Statement I just want to check the solution of the following problem: We have got a string whose length is l and fundamental frequency is f. This string is clamped at a point 0.25l. What are possible frequencies of oscillations of this clamped string? The Attempt at a Solution...
  20. G

    Matter Waves As Standing Waves

    IN an atom why the matter waves associated with electron is regarded as standing wave having varying amplitude within a region and zero outside the region
  21. Y

    How Do You Calculate Harmonics in a Flute?

    [SOLVED] Help regarding standing waves a.The flute player is very musical and produces a pure tone of frequency f=600Hz. For the flute to be in 1st harmonic, what is d where d is the length of the flute? b.By How much has d to be increased to increase the number of nodes by 2? (And keep the...
  22. G

    Standing waves and harmonic waves

    [SOLVED] standing waves Homework Statement A standing wave is a superposition of two harmonic waves described by y1= Asin(kx+wt) and y2= A sin(kx-wt), where A=3.31594 cm, k=10.0531 m-1, and w=18.2212 s-1. Determine the smallest positive value...
  23. S

    Calculating standing waves, given a fruequency? :O

    Homework Statement "Design a tube closed on one end so that it's lowest frequency standing wave is 440Hz. (i.e. determine the length of the tube." Homework Equations Um...I was unsure. I thought maybe...I might use w=2(pi)f...and the function 2A sin (kx) cos (wt), but I epically failed...
  24. F

    Resonance, standing waves and bass

    Why is it that in a room, if you're close to any of the walls the lower frequencies of a sound become louder? Ofcourse, there's an interference pattern in the room. You can hear this by walking around and you'll notice that at some points the bass is weaker and at some points it's stronger (the...
  25. F

    Standing Waves (tension vs. wavelength)

    Homework Statement I'm trying to decode a graph of Tension vs. \lambda^2 of standing waves on a string to understand the actual meaning of the slope. I also need to derive the equation for the line from two expressions: v= \sqrt{T/\mu} v= f\lambda Homework Equations...
  26. R

    Exploring Standing Waves in General Relativity: A Discussion

    I would appreciate if some learned folk could answer these questions to increase my understanding. 1. Does GR support standing wave solutions to the equations? 2. Do physicists study these standing wave solutions? 3. Is it correct to describe GR equations as wave equations? (e.g. as...
  27. A

    Standing waves and length of tube

    Homework Statement A narrow column of air is found to have standing waves at frequencies of 390 Hz, 520 Hz, and 650 Hz and at no frequencies in between these. The behavior of the tube at frequencies less than 390 Hz or greater than 650 Hz is not known. How long is the tube? Homework...
  28. A

    Finding length of tube, air column, standing waves

    Homework Statement A 50-cm-long wire with a mass of 1.0 g and a tension of 440 N passes across the open end of an open-closed tube of air. The wire, which is fixed at both ends, is bowed at the center so as to vibrate at its fundamental frequency and generate a sound wave. Then the tube...
  29. B

    Standing Waves in Strings: Examining Amplitude, Node Number, and Wave Speed

    Homework Statement The figures below show systems of standing waves set up in strings, fixed at both ends, under tension. All of the strings are under the SAME tension and are otherwise identical, EXCEPT for their lengths. The variables in these situations, in addition to the lengths (L) of...
  30. Z

    Understanding the Mechanics of Standing Waves

    I don't understand how standing waves "can exist." A drawing of a standing wave in my textbook shows this (fixed end) I was thinking that if the law of superposition was true then doesn't that mean that ALL the waves should cancel out and you would have a completely straight string (nodes)...
  31. B

    Standing waves in a microwave oven

    Has anyone out there actually tried the kitchen experiment of placing a continuous line of meltable food (i.e. marshmellows/chocholate/cheese etc.) across the bottom of a microwave oven in hopes of finding the antinodes of a standing wave by looking for regions that melt while the rest of the...
  32. M

    What Is the Frequency of Microwaves from This Generator?

    When a reflector is added to the previous setup, as shown in Figure 9 (page 201), a standing wave can be created. We are using a different detector in this case. Measuring the detector output as a function of distance along the goniometer (look it up!), we see that there are maxima and minima in...
  33. E

    Standing Waves on a String with a Free End

    [SOLVED] Standing Waves on a String with a Free End Problem. A string can have a "free" end if that end is attached to a ring that can slide without friction on a vertical pole. Determine the wavelengths of the resonant vibrations of such a string with one end fixed and the other free. By...
  34. A

    The Necessity of Supply: Maintaining Standing Waves

    why there is a need to supply energy to maintain a standing wave?
  35. J

    Understanding Standing Waves: Open & Closed End Formations

    Can somebody explain how standing waves are formed (both open end and closed end) and what exactly they are?
  36. S

    Why Do Standing Waves Require Specific Wavelength Conditions?

    Why do standing waves only exist when \lambda=2L/n? For example why don't they exist when \lambda=4L Not really sure but if \lambda equals 4L then there is only going to be one "loop", I am guessing this has somehting to do with it but I am not sure how to explain it.
  37. C

    Standing Waves on a String (Melde's Experiment)

    The problem is as follows: "A string exhibits standing waves with 4 antinodes when a mass of 200 g is hanging over the pulley (see attached figure). What mass will produce a standing wave pattern with 6 antinodes?" The equations that I have found in the relevant section of the text are as...
  38. L

    Exploring Standing Waves on a Vibrating String: Determining Linear Density

    A string of fixed length L=1.200m is vibrated at a fixed frequency of f=120.0Hz. The tension, Ts, of the string can be varied. Standing waves with fewer than seven nodes are observed on the string when the tension is 2.654N and 4.147N, but not for any intermediate tension. What is the linear...
  39. D

    The Mystery of Standing Waves: How Do Guitar Strings Produce Sound?

    if a standing wave is a wave which transfers no energy, how is it that a guitar string produces a sound? because it produces it via a standing wave, and the sound is sound energy, so where does the energy come from?
  40. L

    Fundamental Frequencies and Standing Waves

    Evening, Ive been having some trouble with questions about fundamental frequencies and labelling nodes and anti nodes in an air column. for example :a tuning fork is placed above a glass tube and then the sound of the air column is adjusted by raising or lowering the glass tube in the...
  41. Amith2006

    Understanding Standing Waves: Clarity on Conditions

    Sir, I have some doubts regarding standing waves. Can anyone who is online now clear my doubts? For the production of standing waves should the 2 interfering waves have the same amplitude, should they be in phase, should they have the same frequency and velocity? I have this doubt because...
  42. R

    End Correction: An Idiot's Guide for Understanding Standing Waves

    Help with understanding end correction I missed a lesson at school on end correction of standing waves in pipes. I have a vague understanding of them, but can anyone give me an idiot's guide to end correction? Most websites I've had a look at haven't been too helpful in explaining it. Now...
  43. D

    Sources of Error in Standing Waves Lab

    I have to write an error analysis for my lab report, but am having some trouble making my sources of error clear and precise. The lab itself was a very basic investigation of the relationship between the tension, frequency, and mass per unit length (mu) in a standing wave pattern. Some...
  44. D

    Standing Waves in Research Industry

    How are standing waves necessary for the research industry? I found some information regarding x-rays, but it's all a little too difficult for me to understand. I just need a short list of fields where standing waves have been useful. Thank you.
  45. D

    Understanding Standing Waves: Interference and Maximum Positions Explained

    I have two questions regarding Standing Waves. [i.] Suppose two speakers face each other with 'x' distance between them. They have = frequency. If i were told to find the points of minimum or maximum interference (or sound pressure amplitude) between the speakers, what excactly am i...
  46. D

    Waves: Standing Waves, Superposition, etc.

    1.) S and P waves, simultaneously radiated from the hypocenter of an earthquake, are received at a seismographic station 17.3 s apart. Assume the waves have traveled over the same path at speeds of 4.50 km/s and 7.80 km/s. Find the distance from the seismograph to the hypocenter of the quake...
  47. B

    Can someone explain how plucking a guitar string produces multiple harmonics?

    When a musical string (guitar etc) is struck a standing wave the length of the string is set up with a frequency X. Also many harmonics are set up with frequencies 2X, 3X, 4X... From my physics textbooks I can understand how by shaking a piece of string (with one end fixed) at the right...
  48. R

    Finding Standing Waves by Adding Two Waves

    I have two waves in a string. One of them is given below, where x is in cm and t is in seconds. y=40cos\frac{\pi}{4}\((0.5x-4t-0.4) I have to find second to produces standing waves when added to the first wave. I know how to add two waves were they are given. Can I get hint on this one...
  49. A

    Density of standing waves in a cavity

    Why is the density of standing waves in a cavity G(f)df=((8*pi*f^2)/(c^3))*df? Also that formula looks weird... doesn't look like it has anything to do with density...
  50. A

    What is the Simple Quantity That Determines Standing Wave Energy?

    The expression T(tension)/(mu*f^2) shows that no matter what the tension, and frequency are, as long as there are the same amount of nodes in the string, the ratio is always the same. The reason that the ratio in the previous part always comes out the same, regardless of which of the many...
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