What is Standing waves: Definition and 259 Discussions

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

    Standing waves on a composite string

    Homework Statement Two strings are joint together, then their other ends are fixed. What is the lowest frequency that must be applied by an external source in order to produce a standing wave on the composite string, with a node on the junction of the two strings? The lengths of the two...
  2. P

    Calculating Standing Wave Nodes: Loudspeaker Distance and Frequency

    Hello All, I have been trying to solve the following exercise but I can't get my head around it: Two loudspeakers are 24m apart and they produce sound at a frequency of 1000Hz, assume speed of sound is 330m/s, what is the distance between each node? I don't undertand it, should I imagine...
  3. M

    Velocity and frequency of standing waves, number of nodes

    Homework Statement A string of mass .03 kg and length 2 m is fixed at one end, and driven with an oscillator at the other end. The oscillator induces traveling waves on the string of the form y=A sin (kx-ωt) which traveled down the string, hit the fixed end, and get reflected back as a wave...
  4. T

    Understanding Standing Waves: Mass Density & Harmonics

    If I have a standing wave, what does doubling the mass density do to the amount of harmonics that are present?? What about quadrupling the mass density? *The standing wave is fixed with a consistent frequency. λ=1/f √(F/μ) I can't get this to work out. I don't think it is going to be...
  5. T

    Standing Waves Theory Question

    Suppose that you were to apply just enough mass so that four "loops" (harmonics) are visible on a standing wave. If the mass density of the string were to double, how many loops (harmonics) if any would be visible? What about if the mass density were to quadruple? Explain. This was a lab...
  6. J

    Calculating Amplitude of Standing Wave at a Given Point

    Homework Statement Adjacent anti-nodes of a standing wave are 7m apart. The amplitude is 0.5m and period 0.05 seconds. Assuming the string is clamped at the position x=0m, y=0m on the left hand side. Find the amplitude at the point 0.29 m from the right of an antinode Homework Equations...
  7. G

    Standing waves and oscillation

    Homework Statement One end of a horizontal string of linear density 6.6*10^-4 kg/m is attached to a small amplitude mechanical 120-Hz oscillator. The string passes over a pulley a distance of l=1.50 m away, and weights are hung from this end. What mass m must be hung from this end of the...
  8. S

    What happens to energy in standing waves?

    Suppose I have a string that has completely no motion. at t=0, I give it energy, two waves. at t=t'. I see destructive interference from the two waves. question: At t=0, the net energy must be positive, >0, then at t=t', where is the energy? (let the waves "meet" at x=L, most of the...
  9. K

    Standing Waves on a Violin String

    Homework Statement A violinist places her finger so that the vibrating section of a 1.00 g/m string has a length of 40.0 cm, then she draws her bow across it. A listener nearby in a 20oC room hears a note with a wavelength of 60.0 cm.Homework Equations Wavelengthm = (2L/m) f1 = (v/2L) =...
  10. B

    Standing waves - which instruments are closed-closed, open-open, or open-closed?

    Homework Statement Okay. So I'm sort of confused about the concept of determining whether an instrument is closed-closed, open-open, or closed-open.ie. a flute, guitar, sax, oboe, clarinet. For example, is a clarinet a closed-open instrument because your mouth covers the entire mouth piece and...
  11. E

    Limit to number of standing waves in pipes?

    Homework Statement This is a conceptual question I had not related to a specific problem- so I know with each higher harmonic in pipes that the frequency increases a certain amount (the fundamental frequency- and that in pipes closed at one end skips the even harmonics). However I also know...
  12. S

    Fermat's Principle, Fourier Analysis, Standing waves, Normal Modes

    Can someone provide me a link that explains and provides a proof for the following principles: 1. Fermat's Principle that light always takes the path that minimizes the time taken 2. Solution to a Fourier Series and why all periodic motion can be represented as an infinite sum of sines and...
  13. V

    Standing Waves - Loud and Soft spots

    Ok, I've got a conceptual issue that I can't seem to resolve. Basically, as far as I know, standing waves can be visualised as displacement standing waves or pressure standing waves and I know that pressure nodes are displacement antinodes and vice versa. However, I've been told that pressure...
  14. J

    The Fundamental Principle of Standing Waves: Is it all about phase?

    I have a question about standing waves. Is this what a standing wave is: a wave produced by a propagating wave and a reflected wave, resulting in a wave of zero propagation. A standing wave is produced, at a particular point, by the two propagating waves and it is simply a superposition of...
  15. N

    Exploring the Relationship Between Microwave Wattage and Standing Waves

    Hey, I am looking for information on the relationship between microwave wattage and standing waves. Does the wattage increase/decrease the size of the wave? Does wattage increase the frequency of the wave? I am also looking the relationship between the time a microwave is operating and...
  16. S

    How do standing waves and resonance relate in a speaker?

    Hi I am actually confused on the relation of standing waves and resonance. I know that standing waves are fromed when two waves of equal amplitude and frequency (one traveling and the other reflected or both traveling waves ) are superimposed in each other. This is the case when we also...
  17. A

    Standing waves hanging in pulley problem

    In the calculation of the theoretical speed vtheo. = √(F_T/μ) (7), the mass associated with the length of the string hanging over the pulley was not taken into account. Suppose that the length of string hanging over the pulley is 20cm and that the hanging mass is 100 grams. What percentage...
  18. H

    [Waves] Standing waves problem (possibly )

    Homework Statement The A-string (440Hz) on a piano is 38.9cm long and is clamped tightly at both ends. If the string is under 667-N tension, what is its mass?Homework Equations \lambda = vT \mu = mass/length v = \sqrt{F/\mu}The Attempt at a Solution I don't really know which equations to useI...
  19. P

    Understanding Standing Waves: A Guide for SAT II Physics

    Homework Statement So I am studying SAT II physics by myself and I don't really understand how standing waves form. I understand that they are formed by the interference of the two traveling waves which results in complete destructive interference at some points, and complete constructive...
  20. LarryS

    Massive Particles and Standing Waves

    Massive particles have a rest energy, m0c2, and therefore a matching rest or intrinsic frequency. So, does that mean that one massive particle at rest in one dimension is a standing wave? Thanks in advance.
  21. R

    Standing waves in stringed instruments

    Homework Statement Hi, I'm currently doing a project on the physics of music, more specifically physics of stringed instruments. I don't really understand how are standing waves generated and used in stringed instruments. Are the standing waves present in the string, in the sound wave, or...
  22. B

    Exploring Standing Waves: Melde's Experiment & Wave Phases

    I am stuck on a question about standing waves: 'The diagram below show's Melde's experiment and demonstartion of a stationary wave on a string' The string has 3 full wavelengths shown, and 3 points are marked: Point A is on an antinode, Point B is on the same antinode, but very...
  23. E

    Energy in standing waves and nodes

    Suppose that two identical waves travel in opposite directions. We know that a stationary wave is creating. How energy passes from the nodes?
  24. S

    Standing waves demo using a string

    im trying to demonstrate a standing wave using a string..can anyone help me with ideas on how to preform such demonstration.
  25. Z

    What is the relationship between standing waves, tension, and velocity?

    Homework Statement see question 2a, b Homework Equations a) v=f(wavelength) b) v= sqrt(F/(m/L)) The Attempt at a Solution a) f=2.5 Hz, t=1.0 s and one wavelength on the graph is I guess 0.4 m? v=2.5(.4)=1 m/s b) f=5.0 Hz, tension same v= sqrt(F/(m/L)) means that a change in frequency will not...
  26. S

    What are the nodal points on a guitar string when plucked?

    Hello guys, I just have few questions about this. [PLAIN]http://www.acousticguitarelectricguitarlessons.com/images/guitar/Electric-Guitar-Parts.jpg Now I understand how a standing wave is formed. However I'm unsure what the nodal points are if I pluck an open string. Is it the...
  27. H

    Standing Waves in a closed pipe

    So confused about standing waves in a closed pipe, which is open at one end and closed at the other. The closed end has a node while the open end has an antinode. To figure the wavelength, i use the formula: Lambda = 4L/n where n is the number of harmonic and can only be odd integers...
  28. A

    Is There Average Power Transfer on Standing Waves?

    Is average power transfer at any point on a standing wave zero? The attempt at a solution: Yes I do think so as power is not transferred across nodes and antinodes hence there is no net energy transfer so average across ANY point should be zero.
  29. W

    Superpositon and Standing Waves problem

    Homework Statement A child has an ear canal that is 1.3 cm long. At what sound frequencies in the audible range will the child have increased hearing sensitivity? Homework Equations for open-closed tube, f= m(v/4L) The Attempt at a Solution I need two frequencies since the question...
  30. L

    Standing Waves: Same Amplitude & Frequency, Opposite Directions?

    Homework Statement Am I right when i say, "Standing waves are produced by the superposition of two waves with the same amplitude and frequency, and opposite propagation directions". If I am then why would it not be, the same amplitude and direction of propagation, but different...
  31. S

    Standing Waves on a Guitar String

    Homework Statement Learning Goal: To understand standing waves, including calculation of and , and to learn the physical meaning behind some musical terms. The columns in the figure (Intro 1 figure) show the instantaneous shape of a vibrating guitar string drawn every 1 . The guitar...
  32. K

    Physics Superposition and Standing Waves (ch. 18)

    Homework Statement A 6.70 kg object hangs in equilibrium from a string with a total length of L = 5.30 m and a linear mass density of µ = 0.00100 kg/m. The string is wrapped around two light frictionless pulleys that are separated by a distance of d = 2.00 m. (visual is attached) The tension...
  33. S

    Standing waves - True or false?

    Homework Statement Consider standing waves in an organ pipe. True or false: 1. In a pipe open at both ends, the frequency of the third harmonic is three times that of the first harmonic. 2. In a pipe open at both ends, the frequency of the fifth harmonic is five times that of the...
  34. S

    Calculating Properties of a Standing Wave

    Homework Statement The wave function for a certain standing wave on a string that is fixed at both ends is given by y(x, t) = (5.00 cm) sin (2.50 m^(− 1)x) cos (500 s^(− 1)t) A standing wave can be considered as the superposition of two traveling waves. 1. a. Give the speed in m/s...
  35. C

    Resonance (standing waves) in glass tube with water

    Homework Statement The water level in a vertical glass tube (length 1 m) can be adjusted to any position in the tube. A tunning fork vibrating at 660 Hz is held just over the open end of the tube. calculate at what position of the water level will there be resonance (standing waves) in the...
  36. P

    Standing waves and microwave ovens

    Homework Statement With a wavelength of 12cm, how do I show that the microwave frequency is approx. 2.5GHz? Homework Equations v=f x lambda The Attempt at a Solution I'm confused about the wave speed bit...
  37. E

    Finding Standing Waves of a Certain Disperssion

    Homework Statement I have a system of infinite particles which when stationary are parted with distance a. Their movement is described with mu^{..}_{n}=\alpha(u_{n+1}+u_{n-1}-2u_{n} From which (assuming the solution is an harmonic wave) I got the dispersion...
  38. K

    Do Solid and Hollow Metal Rods Produce Different Standing Wave Patterns?

    Hello friends, I have done some research on the Internet about producing standing waves in a metal rod, and how the various harmonics frequencies are being derived. I have two questions that i wish to discuss here: 1. Is the pattern of standing waves and method of formula derivation the...
  39. U

    Understanding Standing Waves at 60 Hz and 0.4 m Wavelength

    Homework Statement Draw a sketch of of a standing wave created by a string fixed at two ends, the frequency is 60 Hz, the wavelength is 0.4 m. Draw a profile with times t=0, T/4, T/2, 3T/2 Homework Equations period= 1/frequency, The Attempt at a Solution i know that at t/4, you...
  40. A

    Standing Waves: λ, Mode #, Nodes & Antinodes

    2.2 Suppose you have a string 8 meters long. Briefly explain why it will be possible to set up standing waves with λ= 2 meters but NOT with λ= 3 meters. 2.3 Suppose standing waves of wavelength λ= 3 meters are established in a rope 6 meters long. i. What mode number is this? ii. Not counting...
  41. O

    Traveling and Standing Waves in Quantum Mechanics

    Homework Statement A wave in quantum mechanics is represented by Aei(kx-\omegat). Show that a standing wave looks like 2iAe-i\omegatsin(kx) by subtracting two waves moving in opposite directions. (Hint: make the k negative in one of the waves) Homework Equations As far as I know, the 2...
  42. P

    Phase difference in standing waves

    Homework Statement We have the standard standing wave equation, y=2Acos(2\pi \frac{x}{\lambda})sin(2\pi \frac{t}{T}). We must prove that if two x-positions on the wave have an even number of nodes between them, they have a phase difference of 0, whereas in the opposite condition, they have a...
  43. P

    Electromagnetic standing waves measurement

    Do you get electromagnetic standing waves? If so, do the electric and magnetic fields not cancel each other because of their opposite direction in the standing wave? Can such a thing be measured?
  44. P

    Standing waves, linear density

    Homework Statement In Fig. below, a string, tied to a sinusoidal oscillator at P and running over a support at Q, is stretched by a block of mass m.The separation L between P and Q is 2.30 m, and the frequency f of the oscillator is fixed at 142 Hz. The amplitude of the motion at P is small...
  45. K

    Standing waves and maximum intensity?

    Homework Statement "Two loudspeakers emit sound waves along the x-axis. The sound has maximum intensity when the speakers are 27.5 cm apart. The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 60.5 cm. What is the wavelength of the...
  46. K

    How Do Nodes Function in Standing Waves with Fixed and Open Ends?

    Homework Statement I don't have an actual problem to solve, it's more of a conceptual problem. I'm trying to understand harmonics and standing waves, and how the nodes work out, but it's very confusing. (1) If a wave is FIXED at both ends, for the fundamental or 1st harmonic, does it...
  47. K

    Finding the Longest Wavelength of Standing Waves on a 254.0 cm String

    Homework Statement What is the longest wavelength for standing waves on a 254.0 cm long string that is fixed at both ends? Homework Equations The Attempt at a Solution When x = L (length of string): k(n) = n*pi / L wavelength (n) = n*pi / k(n) I got the answer, I just...
  48. P

    Examples of travelling and standing waves

    Homework Statement Give an example of a traveling wave AND a standing wave for: 1 - Disturbances along a rope 2 - Sound 3 - Light Homework Equations None I can think of The Attempt at a Solution Hi, could someone please tell me if these are correct and, if not, what could I say...
  49. G

    Why Does the Pulley Section Lack a Standing Wave in the String Experiment?

    Here's one for you guys. I've done some research and I couldn't find an exact answer to my question... In the experiment shown here: http://www.itc.csmd.edu/mth/ahouser/PHY1010/labs/Lab10StandingWaves.pdf Why is there no standing wave on the segment of the string between the pulley and the...
  50. T

    What is the equation for standing wave patterns and why is the solution 0?

    Homework Statement Hi everyone. I am working on a physics research paper on Standing Wave Patterns and the physics of a viola. I found this formula for standing wave patterns and am having trouble making sense of it. When I tried, I got sin(0) which is 0 making the whole thing 0. Is this a...
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