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. Saxby

    Conservation of energy in standing wave

    Homework Statement A standing wave is produced by small transverse oscillations of one end of a taught string stretched between an oscillator and a fixed point. The frequency of oscillation is adjusted to be resonant at the third harmonic. The amplitude of the string's viabration is very...
  2. S

    What Is the Lowest Frequency for a Standing Wave in a Compound Wire?

    Homework Statement An aluminum wire of length l1 = 60cm, cross section area 1.00 x 10-2cm2, and density 2.60g/cm3, is joined to a steel wire of density 7.8g/cm3 and same cross sectional area. The compound wire loaded with a block of mass m = 10kg is arranged as shown so that the distance...
  3. A

    Exploring Standing Wave Speed: Understanding the Concept and Formula in Physics

    My Friend and I were discussing standing waves and I made problem about speed, inspired off a concept taught in my Physics book: v = \sqrt {\frac {F_T}{m/L}}. My Friend asked a very valid question: "How in the whole can you defined speed of a standing wave when it's not changing position?" - He...
  4. J

    Waveguide standing wave pattern

    Hi everybody, that's my question, I have been measuring the standing wave pattern within a waveguide (X band) using a slotted line, I put a short circuit termination and the theory said that we expect a rectified sine, but I don't get that, my result is in the picture I can't explain my...
  5. B

    Has path of a standing wave confined in a metal box been measured and described?

    Has path of a standing wave confined inside a metal box been measured and described? I'm thinking path is circular, or, oscillates/bounces back and forth like a pendulum. I'm thinking of a standing wave moving inside a metal rectangular box. Has the path of a standing wave inside a...
  6. P

    Can Standing Waves Form with Different Amplitudes or Frequencies?

    I came across a question about wave from univeristy physics (sears n zemansky) and the question was 'can a standing wave.be produced on a string by by superposing two waves traveling in opposite direction with same frequency but different amplitudes? And same amplitude but different...
  7. P

    Frequency of a standing wave on a string

    Homework Statement a 50m length of string with mass 0.0175 kg has waves traveling at 112 m/s. There is a mass attached to the string, 0.45 kg that is creating a 4.41 N tension. What is the frequency of the string vibrator? Homework Equations v=f*λ f= [√T/(m/L)]/2L The Attempt at a...
  8. B

    Standing Wave in superposition equation problem

    A string with tension F Newtons, mass m kilograms, and length L meters is clamped at each end (y=0 at x=0 and x=L). At time t=0, the displacement in the y-direction for each point x on the string is defined as: y(x, t = 0) = 2 sin ( 2πx/L) + 3 sin (πx/L) = y1(x, t = 0) + y2(x, t = 0) (a)...
  9. D

    Is sine*sine a form of a standing wave?

    What kind of wave is Asin(kx)sin(wt)? Using trig functions, I've rewritten it as Bcos(kx-wt) - Bcos(kx+wt) So it sort of looks like it's a standing wave in that it's a superposition of two waves traveling in opposite directions with equal amplitude and wavelength, yet I'm unsure since...
  10. S

    Standing wave interference patterns on liquid metals

    Hi, first post, so take it easy on me, I've had an idea for producing metallic objects with high surface area for several years, but lack the necessary physics knowledge to act on it or, really, inclination (and money) to go through years of school to gain such. The idea is as follows: A...
  11. M

    How to produce a standing wave question

    Homework Statement using a wire of length L= 1 M with both ends fixed, can you produce a standing wave with the following wavelengths? Explain why or why no. a. 30 cm: b. 1m : c. 75 cm : d. 2 m : Homework Equations L=n. (λn/2) The Attempt at a Solution 1m= n. 30 cm/2 ?
  12. F

    Velocity and acceleration of a standing wave

    Homework Statement A string with both ends held fixed is vibrating in its third harmonic. The waves have a speed of 192m/s and a frequency of 240 Hz. The amplitude of the standing wave at an antinode is .4cm. Calculate the maximum transverse velocity and the maximum transverse acceleration...
  13. P

    A standing wave on a string with a mass hanging on it

    Homework Statement A sphere of mass M=6.85 kg is supported by a string that passes over a light horizontal rod of length L=0.73 m. Given that the angle is θ=22.3° and that the fundamental frequency of standing waves in the section of the string above the horizontal rod is f=246 Hz...
  14. M

    The Typical diagram of a standing wave

  15. P

    Calculating Wavelengths in de Broglie's Standing Wave Condition

    Homework Statement de Broglies standing wave condition demands that an inegral number of wavelengths fit into the circumference of the Bohr orbit. How many "interal wavelengths" are there in the fourth exited state of Be3+? Homework Equations n lambda = 2 pi r The Attempt at a...
  16. Y

    Waht does standing wave with both ends open has 396hz mean?

    Homework Statement A standing wave in a pipe with both ends open has a frequency of 396 Hz. The next higher harmonic has a frequency of 662 Hz.(a) Determine the fundamental frequency. answer: 266 Hz (b) How long is the pipe? answer : 0.645 m The Attempt at a Solution...
  17. C

    Prof that it is not possible to get a standing wave.

    Homework Statement As in the Title starting from two planewaves with the same amplitude, but different frequency. Homework Equations Starting from Ae^{i(kx +\omega_1 t)} + Ae^{i(kx +\omega_2 )} The Attempt at a Solution I got as far as Ae^{i(kx +\omega_1 t)} + Ae^{i(kx +\omega_2 )} =...
  18. J

    Energy of interfering standing wave

    Okay, I know that I should know this, but its just been a while so here it is: I have a few emitters at 2.5 GHz at different points on the edge of a sphere of water. I want to find the RMS energy transmitted into the water in the sphere. Ideally by moving emitters/adding a phase delay, I...
  19. M

    Tension in a wire due to a standing wave

    Homework Statement Question 8 A 2m long steel wire is mounted in an insulated bath of water containing 2000 litres of water. (a) If the bath is a rectangle 2 m long and 1 m wide, what is the depth of the water The wire vibrates with a fundamental frequency of the G above middle C (392 Hz)...
  20. D

    Standing Wave in Closed Tubes Lab

    1. http://img856.imageshack.us/i/scanpic0001.png/ using tuning forks, you're supposed to choose 7 notes and find the frequency and length then find an approx speed for sound. we did this with logger pro and a USB microphone device and glass tubes. i plugged in my data to this eq'n: fn =...
  21. A

    Which Method Should Be Used to Calculate Energy in Standing Wave Formalism?

    Homework Statement If you have seen the treatment of calculation of density of states using standing wave formalism in Modern Physics by Arthur Beiser, their are these observations of which i am not completely convinced, with wavelength fixed, he transforms wavelength into energy, using...
  22. B

    Determine the frequency of a standing wave with Young´s modulus?

    Note: This is a laboration assignment. Homework Statement I want to theoretically determine the frequencies of the standing waves that occurs in a Chau gong when exposing it to a camera flash (Nikon sb-900) from a given distance. These shall then be compared to the frequencies obtained from...
  23. D

    Fundamental frequency of a standing wave

    Homework Statement A standing wave is established in a string of length 150 cm fixed at both ends. The string vibrates in four segments when driven at 140 Hz. Find the wavelength in meters. Find the fundamental frequency. Homework Equations L = Nλ v = fλ The Attempt at a...
  24. E

    Closed tube standing wave

    Standing waves have a fundamental frequency equal to 4x the length of the pipe if the pipe is closed at one end and open at the other end. So, blowing across the top of a 33.2 cm bottle should produce a fundamental frequency of v/4L or about 340/1.2= 283 hz. When I record the sound produced...
  25. J

    Find wavelength for a standing wave

    Homework Statement Two sinusoidal waves with identical wavelengths and amplitudes travel in opposite directions along a string with a speed of 10 cm/s. If the time interval between instants when the string is flat is 0.50 s, what is the wavelength of the waves? Homework Equations v = w/k =...
  26. J

    How Does Changing a Hole in a Pipe Affect Its Resonant Frequency?

    This is more a clarification concerning harmonics, I think. :) The problem is thus: If a hole in a pipe changes the resonant frequency of the pipe by a factor of 2, what is the new frequency. My confusion: I think this is a simple harmonics question, but I am confused by the term...
  27. P

    Can a Longitudinal Oscillator Be Seen as a Standing Wave?

    Hello there! I was thinking is it possible to observe a simple longitudinal oscilator (lets say a mass on a string) as a standing wave? Thinking maybe as wave which has a front 4 times than the size of the string. So when we excite the string, we are actually emmiting a wave. One...
  28. T

    Specific Acoustic Impedance of Standing Wave

    Homework Statement Find the specific acoustic impedance for a standing wave p=Psin(kx)exp(jwt) where p is a complex variable.Homework Equations z = p/u (all variables are complex) u = (A/rho_sub_0*c)*exp^(wt-kx)The Attempt at a Solution Approaching this problem it seems that I have all of the...
  29. C

    Predicted Amplitude for Standing Waves on a String: Can It Be Calculated?

    Homework Statement One end of a string is attached to a vibrating "reed" that vibrates at 120 Hz. The other end is passed along a pulley stationed 1 meter away from the vibrating reed. Different masses are hung from the end of the string that passes over the pulley in order to create a...
  30. P

    Conceptual quest on standing wave

    How can we predict whether, a wave ( say a one dimensional string wave) traveling in any direction (say +x) after reflection from the fixed end, forms a standing wave in the medium or not (here string)? I do not understand why the length of stirng should be integral multiple of wavelength(...
  31. T

    Guitar string - standing wave question

    This question is for a conceptual physics class (no trig involved). 1. The wave speed on a tightened guitar string is 880 m/s. What is the shortest length of string that will produce standing waves of 440-hertz frequency? (Be very CAREFUL!) a. 0.5m b. 1.0m c. 1.5m d. 2.0m e...
  32. S

    Standing wave detection using a microphone

    Hi I am trying to develop a standing wave inside a rectangular cavity and detect it using a microphone.In one wall of the cavity ,I placed a loudspeaker and driving it at a frequency of 8.3 Khz. The chanel has a thickness for half wavelength standing wave. I am trying to detect the nodes...
  33. A

    What Can We Learn About Wave Speed from a Vertical Standing Wave?

    Homework Statement A spring is held vertically between two supports separated vertically. That stationary wave set up looks like this: http://img690.imageshack.us/img690/9417/80122335.jpg Deduce what you can about the speed of the waves in the spring. (Note that the wave pattern is slightly...
  34. P

    Energy in a Fundamental Standing Wave Vs. The Energy in its Harmonic Waves

    I am seeking to understand the relationship of energy within a standing wave vs. the energy in its first three harmonics. Is the energy latent within the fundamental wave the same as the energy in its first three harmonics, or is the energy and exponential increase. IE How much energy is...
  35. A

    Standing Wave pattern on an open circuited transmission line with length λ/4

    Here's a scenario about which I have doubt. Consider a transmission line which has a length λ/4 and which has open circuit at load end. The source resistance is zero. The source voltage be Vs and the source frequency is sufficiently high to be considered as high frequency application . The line...
  36. S

    Inductive reactance – Circular loop with N lambda standing wave

    Has anyone come across, or may be able to point me in the direction of a method for evaluating the inductive reactance of a circular loop when the wavelength of the applied signal is significantly less than the conductor length of the loop - and more particularly when; A. The driven...
  37. S

    Inductive reactance – Circular loop with N lambda standing wave

    Has anyone come across, or may be able to point me in the direction of a method for evaluating the inductive reactance of a circular loop when the wavelength of the applied signal is significantly less than the conductor length of the loop - and more particularly when; A. The driven wavelength...
  38. J

    Standing Wave Equation: Exploring Y = 2Asin(\omegat)cos(kx)

    My lecturer said that a standing wave is formed when two waves that travel in the opposite have the same frequency. He said that if the waves are y1 and y2, then the resulting wave y can be given as the sum: y = y1 + y2. y = Asin(\omegat - kx) + Asin(\omegat + kx). (1) Where the...
  39. S

    Infinite well's standing wave

    SHOW THAT THE INFINITE WELL'S STANDING-WAVE FUNCTION CAN BE EXPRESSED AS A SUM OF TWO TRAVELING WAVES OF THE FORM Ae^i(kx-wt) Homework Equations The Attempt at a Solution
  40. E

    Finding the relationship between wave speed and tension in a standing wave

    Homework Statement The problem is the same as the title; to find the relation between wave speed and tension for a standing wave in a string. (Fixed ends) Given data (from the experiment) String length = 1.62m, mass is negligible Frequency = 48.2 Hz Basically one end of the string was...
  41. P

    Calculating Mass Using Standing Waves on a Suspended Wire

    Homework Statement When mass M is tied to the bottom of a long, thin wire suspended from the ceiling, the wire's second-harmonic frequency is 200 Hz. Adding an additional 1kg to the hanging mass increases the second-harmonic frequency to 245 Hz. What is M? f_{2} = 200hz, m = M f_{2} = 245hz...
  42. D

    Exploring Standing Wave Velocity: Human Error or Physics?

    I just completed a lab in which we created standing waves in a fixed length of pipe using a function generator. An oscilloscope was used to measure the amplitude of the waves. The frequency was changed until a resonant condition was met, and then the location of all the nodes/antinodes was...
  43. P

    How Many Harmonics in a 4-Node Standing Wave?

    Homework Statement A standing wave is set on a string by a vibrating the string at one end. You count 4 nodes on the standing wave. Which harmonic have you produced? The Attempt at a Solution I thought it was 3rd harmonic,but my teacher put 2nd harmonic whos right?
  44. Y

    Understanding Standing Wave Basics for Non-Physicists

    As I https://www.physicsforums.com/showthread.php?t=283482", I'm struggling with physical basics of vibration in rods as a non-physicist. If someone would be kind enough to explain in simplest possible terms, I would like to understand two things: 1. What is the relation between standing...
  45. E

    Why is Half a Wavelength the First Harmonic in Standing Wave Harmonics?

    Why does half a wave length and not a full wave length constitute the first harmonic? v=\lambdaf because a standing waves can be made with two half waves traveling in opposite directions?
  46. P

    How Does Changing Boundary Distance Affect Node Addition in Standing Waves?

    Homework Statement Consider standing waves that are reflecting between two identical boundaries. If the distance between the boundaries is increased by a distance delta L, what value of (delta L / lambda) will add one additional node (and antinode) to the standing wave pattern? (Assume that...
  47. G

    What is the Amplitude of a 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 0.386 m. The maximum transverse acceleration of a point at the middle of the segment is 9000 m/s^2 and the maximum transverse...
  48. E

    Why Does the String Behind the Node Stop Oscillating in a Standing Wave?

    Homework Statement "A standing wave in the form of a string attached to a driven tuning fork is created. We then move the furthest boundary point to a node somewhere along the string. The node of course was originally at rest by definition. The string behind the node with the boundary point...
  49. M

    Can Two Waves of the Same Frequency Create a Standing Wave on a String

    can we get a standing wave in a string if we affect with with two waves with same frequency on it . thanks...
  50. M

    Conceptual Standing Wave Question

    Homework Statement If you take snapshots of a standing wave on a string, there are certain instants when the string is totally flat. What has happened to the energy of the wave at those instants? The Attempt at a Solution I'm assuming that nothing has happened to the energy. At...
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