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. T

    Musical Tube and String (Standing wave)

    Homework Statement A brass tube of mass 20 kg and length 1.1 m is closed at one end. A wire of mass 9.6 g and length 0.4 meters is stretched near the open end of the tube. When the wire is plucked, it oscillates at its fundamental frequency. By resonance, it sets the air column in the tube...
  2. V

    Standing Wave Question: Wavelength of Resultant Wave with Two Opposing Waves

    Homework Statement If a standing wave is produced by two identical waves traveling in opposite directions, is the wavelength of the resultant wave simply the wavelength of the original wave? Homework Equations ysin(kx)cos (wt) The Attempt at a Solution I'm pretty sure it...
  3. H

    What Frequencies Form Standing Waves in a Microwave Cavity?

    A microwave generator can produce microwaves at any frequency between 10 GHz and 20 GHz. The microwaves are aimed, through a small hole, into a "microwave cavity" that consists of a d = 8 cm-long cylinder with reflective ends. Select all frequencies from those tabulated below which will...
  4. M

    Time and amplitude in a standing wave.

    1. A string vibrates in its 3rd harmonic standing wave pattern. The mass and length of the string are given. Also given is the tension in the string and the transverse velocity of the string at the antinode located at x = Length/2 when the standing wave has no displacement at t = 0.00s M =...
  5. K

    What are the Water Heights for a Standing Wave in a Tuning Fork and Tube Setup?

    Homework Statement A 1.0m long vertical tube is filled with water. A tuning fork vibrating at 580Hz is held over the open 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...
  6. N

    Calculating Next 3 Harmonics of a Standing Wave

    Homework Statement Given the first harmonic, with length L, of a certain standing wave, what is the process for coming up with the next 3 harmonics for it?Homework Equations velocity = wavelength * frequencyThe Attempt at a Solution I don't understand how to draw the "next harmonic". I've come...
  7. S

    What Is the Correct Velocity of the Standing Wave?

    Homework Statement The standing wave in the picture is oscillating at 100 Hz. What is it's velocity? Homework Equations Velocity=(wavelength)(frequency) I believe is the equation that applies here. The Attempt at a Solution The wavelength from the picture appears to be...
  8. M

    Finding Mass for a Standing Wave in a Horizontal String

    Homework Statement One end of a horizontal string of linear density 4.7 multiplied by 10-4 kg/m is attached to a small-amplitude mechanical 58 Hz vibrator. The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11-48. Assume the string at the...
  9. M

    Electromagnetic wave reflects off a surface at a 90 degree angle. Standing wave?

    What happens when an electromagnetic wave reflects of a surface at an 90 degree angle and continues moving along the same path as it came from? Will the two waves that are moving in opposite direction interfer with each other to from a standing wave pattern? This seems to be the case when...
  10. A

    Standing Wave Energy: Find Total Mech. Energy

    Homework Statement A standing wave is maintained in a homogenous string of cross-sectional area a and density \rho . It is formed by the superposition of two waves traveling in opposite directions given by the equations y1 = Asin(wt-kx) y2 = 2Asin(wt +kx) Find the total mechanical energy...
  11. C

    Fundamental standing wave problem

    Homework Statement A 40-cm long string, with one end clamped and the other free to move transversely, is vibrating in its fundamental standing wave mode. If the wave speed is 320 cm/s, the frequency is: A) 32 Hz B) 16 Hz C) 8 Hz D) 4 Hz E) 2 Hz Homework Equations v = \lambdaf L =...
  12. K

    Energy stored in a standing wave

    I'm trying to find the energy stored in a standing wave on a string. My book suggests to find the maximum kinetic energy for a small segment of the sting, and then integrate over the string. I find this strange, because the kinetic energy is certainly not at its maximum all over the string...
  13. S

    How does changing length and mass affect the frequency of a vibrating string?

    I found that if you have a stretched wire under tension that if you a) change the length the change in frequency is directly proportional to the change in length. b) change the mass the change in frequency is inversely proportional to the change in mass. Does anyone know how to back...
  14. P

    Find Minimum Frequency to Establish Standing Wave on Wire

    Homework Statement A student wants to establish a standing wave on a wire 1.7 m long clamped at both ends. The wave speed is 587 m/s. What is the minimum frequency she should apply to set up standing waves? Homework Equations Not sure...need help here? :) The Attempt at a Solution...
  15. B

    Frequency of a Standing Wave on a String

    Homework Statement The frequency of a standing wave on a string is f when the string's tnesion is T. If the tension is changed by the small amount deltaT, witout changing the length, show tat the frequency changes by an amount deltaf, such that deltaf/f = .5 * deltaT/T Homework...
  16. B

    Find Frequency for Standing Wave with Joint & Pulley Nodes in Compound Wire

    An aluminum wire of length .6 m, cross sectional area of .01 cm^2, density 2.60 g/cm^3, is tied to a steel wire of density 7.8 g/cm^3 and the same cross sectional area. The compound wire is joined to a pulley and then a block of mass 10 kg is tied at the end of the steel wire. Thisi is...
  17. P

    Wavelength and Fundamental Frequency of Standing Wave on 2m String

    A standing wave resonates at 400 Hz with three antinodes on a string tied tightly between two posts 2.0 meters apart. What is the wavelength of this standing wave? What is the fundamental frequency of this string? I tried to draw the picture out, and it looks like the wavelength is just...
  18. B

    Trying to plot de Broglie standing wave.

    Does anyone know how to plot the electron standing wave around a nucleus in Cartesian coordinates? I have tried adding a sine/cosine function to the circle equation but the image does not look correct and I also don’t know how to increase the wave count when n > 1.
  19. D

    Standing wave interference pattern problem

    In a standing wave interference pattern, what distance constitutes a wavelength? For complete destructive interference, what must be true of the wavelengths and amplitudes of the 2 waves? Thx
  20. M

    Effect of Liquid Level on Standing Wave Frequency in a Soda Bottle

    A partially empty soda bottle will produce standing waves in the air above the liquid if you blow across the neck of the bottle. There will be a displacement antinode at the neck and a node at the surface of the soda. What happens if you drink more soda and repeat the experiment? a) no change...
  21. D

    Milo Wolff: Spherical Standing Wave Structure of Matter

    Has anyone heard of Milo Wolff? I recently came upon www.spaceandmotion.com using StumbleUpon, and read the section of quantum theory, and the interpretation of quantum theory using spherical standing waves to describe matter seemed interesting, but I couldn't find anything on it besides that...
  22. ~christina~

    Simple standing wave question- not exactly sure why I can't get answer?

    [SOLVED] simple standing wave question- not exactly sure why I can't get answer?! Homework Statement A particle fingering flute sounds note with frequency of 880Hz at 20 deg celcius(343m/s => sound wave speed) The flute is open at both ends. a) find the air column length b) find the...
  23. T

    Amplitude of Standing Wave in Fundamental Mode

    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 8200 m/s^2 and the max. transverse velocity...
  24. T

    Instaneous Power in a standing Wave

    Homework Statement The instantaneous rate at which a wave transmits energy along a string (instantaneous power) is P(x,t) = =F\frac{\partial y(x,t)}{\partial x} \frac{\partial y(x,t)}{\partial t} where F is the tension. Show that for all values of x, the average power P_a_v...
  25. D

    What is the length of the vibrating section of the violin string?

    Homework Statement A particularly beautiful note reaching your ear from a rare Stradivarius violin has a wavelength of 39.1 cm. The room is slightly warm, so the speed of sound is 344 m/s. If the string's linear density is 0.620 g/m and the tension is 160 N, how long is the vibrating section...
  26. N

    What is the lowest-frequency standing wave

    Homework Statement A 22-cm-long, 1.0-mm-diameter copper wire is joined smoothly to a 60-cm-long, 1.0-mm-diameter aluminum wire. The resulting wire is stretched with 20 N of tension between fixed supports 82 cm apart. The densities of copper and aluminum are 8920kg/m^3 and , 2700 kg/m^3...
  27. S

    Vibrating a 75g Bungee Cord: Standing Wave Formation

    Homework Statement A 75 g bungee cord has an equilibrium length of 1.20 m. The cord is stretched to a length of 1.80 m, then vibrated at 20 Hz. This produces a standing wave with two antinodes. Homework Equations I really am not sure how to approach this using an equation, tried to use...
  28. R

    Standing wave on a guitar string

    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 0.380m. The maximum transverse acceleration of a point at the middle of the segment is 8700m/s^2 and the maximum transverse...
  29. N

    Constructing a Standing Wave Interference Pattern

    Hi, the question was, "Suppose that the wave represented by the graphs interfered with its OWN reflection. Sketch one standing wave interference pattern you would expect to observe. On your sketch, indicate the amplitude of each supercrest and supertrough, and the internodal distance (using...
  30. G

    Analyzing Standing Wave Phase at Points P, Q, R, S, T & U

    Homework Statement A standing wave is set up on a stretched string as shown. At which points will the osciallation be exactly in phase witht that at P? At which points will the oscillation be exactly out of phase with that at P? The points are on the horizontal line. Q at 2 P at 5 R...
  31. Z

    Interrupting a standing wave at a node

    Suppose you have a taut string, and you pinch it firmly at the middle, so that the middle is immobile but the string has the same tension throughout. Then you start vibrating one end of the string. I would think that the wave could not propagate past the middle of the string, because you have...
  32. R

    Understanding Standing Wave Patterns at 50Hz Frequency

    In a standing wave, if the fundamental frequency is 25hz but the frequency that is currently being fed to the string is 50hz how do i determine what the resulting wave will look like?
  33. F

    Combining Two Transverse Waves to a Standing Wave

    Homework Statement Two transverse waves traveling on a string combine to a standing wave. The displacements for the traveling waves are Y1(x,t) =0.0160m sin(1.30m^-1x -2.50s^-1t + 0.30) and Y2(x,t) = 0.0160m sin(1.30m^-1x -2.50s^-1t +.070), respectively, where x is position along the string...
  34. K

    Why Generating a Purely Optical Standing Wave is Impossible

    why is it impossible to generate a purely optical standing wave? thanks in advance
  35. K

    Nodes in the resulting standing wave

    Homework Statement Microwaves of frequency 10^10 Hz are beamed directly at a metal reflector. Neglecting the refractive index of air, determine the spacing between successive nodes in the resulting standing wave. Homework Equations The Attempt at a Solution dont know what to do here
  36. P

    Standing Wave Frequencies in Wire & Pipe: Similarities & Differences

    -Look up or derive the frequencies of the standing waves of a length of wire, L, clamped at the ends and under tension. -What are the similarities and differences between a vibrating string and a resonating pipe? -Does the diameter of the wire matter? -Does the diameter of the pipe matter...
  37. S

    Fundamental standing wave in Closed tube

    Homework Statement You blow across the open mouth of an empty test tube and produce the fundamental standing wave of the air column inside the test tube. The speed of sound in air is 344 m/s and the test tube acts as a stopped pipe. If the length of the air column in the test tube is 14.0...
  38. D

    Standing Wave Problem: Aluminum and Steel Wire Joint with External Source

    an aluminum wire of length L1 = 50.0 cm, cross-sectional area 1.00×10-2 cm2, and density 2.70 g/cm3, is joined to a steel wire of density 7.80 g/cm3 and the same cross-sectional area. The compound wire, loaded with a block of m = 10.0 kg, is arranged so that the distance L2 from the joint to the...
  39. B

    How Does Tension Affect the Speed and Wavelength of Waves in a Guitar String?

    A nylon guitar string has a linear density of 9.0 g/m and is under a tension of 180.0 N. The fixed supports are L = 80.0 cm apart. The string is oscillating in the standing wave pattern shown in the figure. Calculate the speed of the traveling waves whose superposition gives this standing wave...
  40. S

    Standing wave velocity/acceleration

    A string with both ends held fixed is vibrating in its third harmonic. The waves have a speed of 195 m/s and a frequency of 240 Hz. The amplitude of the standing wave at an antinode is 0.350 cm. I have already correctly calculated the amplitude of the string at a point 24 cm from the left of...
  41. A

    Understanding Standing Wave Sign Conventions

    Hi. Okay, this has been driving me crazy. When combining two given waves into a standing wave equation, how do you know which sign to put in front of the amplitude? All the examples I've been finding seem to contradict each other. Here are three examples from my textbook: 1. Incoming Wave...
  42. P

    Question about transverse standing wave including violin string

    I have a question on this problem 1. 10. A violin string vibrates at 335 Hz when unfingered. At what frequency will it vibrate if it is fingered one half of the way down from the end? For this one I worked out that string is fixed at both ends because its in a violin so I am thinking of...
  43. N

    How Does Changing Tension Affect Standing Wave Patterns and Antinode Formation?

    http://img103.imageshack.us/img103/1306/waves8hu.png Here is my question (2 parts) a) Draw the standing wave that occurs if the string tension is quadrupled while the frequency is held constant. im not sure how these are related, any equation? b) Suppose the tension is doubled while...
  44. S

    How Can I Calculate Tension and Amplitude in Standing Wave Problems?

    Hi I was wondering if someone could tell me if I am heading in the right direction with these Thanks in advance Q1 In an experiment on standing waves, a string 90 cm long is attached to the prong of an electrically driven tuning fork that oscillates perpendicular to the length of the string...
  45. S

    Calculating Wave Function for Standing Wave on String

    Hey! Here is one that I thought would be easy: Two traveling waves move on a string that has a fixed end at x=0. They are identical except for opposite velocities. Each has an amplitude of 2.46mm, a period of 3.65ms, and a speed of 111m/s. Write the wave function of the resulting standing...
  46. R

    Calculating Speed, Amplitude, and Distance in a Standing Wave

    Hi again :biggrin: The first part of my question was stated under "Simple math problem". However, the rest subproblems are no more simple math ones only :rolleyes: I'm given the wave function y(x,t)=4.2\cos(0.2x)\sin(300t). (a) What are the speed and amplitude of the two traveling waves...
  47. H

    What Causes the Pitch Changes in a Spinning Twirler Toy?

    Standing Wave/ Resonanace problem PLEASE HELP! Ok. I've tried to answer this problem so many times now, but I just can't get it. Here it is: A child's toy called a twirler, consists of a tube (like a hose, which is spun in a circle above one's head. It is noted that at certain rates of...
  48. A

    Determining lowest f of standing wave

    If the length of a string with two fixed ends and three loops, along with the wave speed is given, how would you find the lowest frequence for standing waves on that string? I thought that the fundamental frequency determined the lowest frequency. Thanks for your help! -Albert
  49. L

    Calculating Displacement and Speed in a Standing Wave on a String

    Adjacent antinodes of a standing wave on a string are a distance 14.5 cm apart. A particle at an antinode oscillates in simple harmonic motion with amplitude 0.850 cm and period 8.00×10-2 s . The string lies along the + x - axis and is fixed at x = 0. Find the displacement of a point on the...
  50. T

    Standing Wave Problem, What is the mass of the string?

    When the tension is 18 N, a string 2.00 m long has a fundamental frequency of 150 Hz. a.) What is the mass of the string? b.) With what tension must the string be stretched so that it vibrates in three segments at 150 Hz? This is what I came up with: a.) f=v/2L, v=2Lf=2*2*150=600 m/s...
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