standing waves Definition and Topics - 40 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. vel

    Displacement nodes for overtones

    (4 / 3) * (1.8) = 2.4 = lambda 1st overtone: 2.4 / 4 = .6; (2.4 * 3) / 4 = 1.8
  2. M

    Standing waves between two speakers in phase

    The solution provided in the manual poses that the point halfway between the nodes at each speaker is an antinode of pressure (node of displacement) but isn't that a contradiction to the fact that the speakers are in phase? My first thought was that they must interfere constructively and have...
  3. 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?
  4. 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)...
  5. K

    Pressure Waves in an Open Tube

    1. Problem Statement: The pressure in an gas tube of length L stretched along the x-axis is given by P(x, t) = Patm + P1(x, t) + P2(x, t) (1) where , P1(x, t) = 20 [P a] sin (−5.9 x − 1300 t ) P2(x, t) = 20 [P a] sin (5.9 x − 1300 t ) One open end of the air tube is at x = 0m. By how much...
  6. Mohammed Sayanvala

    What do wave crests indicate about a boat's speed?

    Homework Statement *I cannot place the original image due to copyright reasons, but the image above is a good alternative. "Wave crests spread out behind a boat as shown above. What do the wave crests indicate about the boat's speed?" It is increasing. It is less than the speed of the water...
  7. MatthijsRog

    What constitutes a closed end in acoustic resonance in tubes

    Dear all, For my students, I'm currently trying out some experiments they can do to simulate acoustic processes. One of the topics that we will be discussing is that of standing waves. Although I have never done it before--I come from a completely different background--I want to create...
  8. J

    Why do Harmonics Decay Faster than the Fundamental?

    When looking at the FFT spectrum of a sonometer, I noticed that the harmonics decayed faster than the fundamental. Why is this?
  9. 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...
  10. S

    Standing Waves (Instruments) & Interference interpretation?

    Hi, I'm trying to solve two problems related to standing waves and wave interference; while I'm not having difficulty with the actual solving portion, I don't know if I'm interpreting the questions correctly. Question 1: "A violin string is tuned to 460 Hz (fundamental frequency). When...
  11. G

    Dielectrics and standing waves

    How do dielectrics affect the number of modes for standing electromagnetic waves in a box?
  12. Y

    B Is this an accurate description of standing waves?

    Hi all, is my description below a reasonable attempt in explaining how a standing wave forms? The main part I am a bit confused as to how to explain is why the antinodes move up and down. Thanks! A standing wave is formed when energy of a wave of the right frequency is trapped in the system...
  13. Const@ntine

    Standing Waves: Synchronization between a Tube & a Stick

    Homework Statement A wooden stick, part of a musical instrument, which produces a musical sound when hit, oscillates by creating a transverse standing wave, with three antinodes and two nodes (3 "valleys", 2 "ground levels"). The lowest note has a frequency of f = 87.0 Hz, and is produced by...
  14. L

    Phase difference and Standing waves vs Progressive waves

    and Homework Statement Ok, so I am doing As physics at the moment and have been left confused by stationary waves. I have read that between adjacent nodes/ even numbers the phase difference is always 0 and between numbers of does it is pi radians. So in the attatched image why is my textbook...
  15. W

    Flute player initial frequency?

    Homework Statement A flute player hears four beats per second when she compares her note to a 587 Hz tuning fork (the note D). She can match the frequency of the tuning fork by pulling out the "tuning joint" to lengthen her flute slightly. What was her initial frequency? Homework Equations Not...
  16. O

    Python Wave on string: How can I create a traveling triangle pulse?

    I have the following program that moves a wave on a string with fixed ends. The program solves the wave equation given a initial condition wave. The initial condition is a triangle wave splitting into two pulses. Here is the code written in Python: from numpy import * from matplotlib.pyplot...
  17. O

    Why plucking of string creates two pulses?

    When we pluck a string and a triangle is formed. Why does this triangle form into two opposite moving pulses? If we have reflective edges the two pulses will reflect, invert and superposition into the same triangle wave on the under side of the string. Let's say we have no dampening. I think...
  18. Marcus95

    Number of Different resonances in a closed Box

    Homework Statement Show that the possible resonance frequencies in a 3D box with side a are constant multiples of ##(l^2+m^2+n^2)^{1/2}##, where l, m and n are integers. Assume that the box with sides a is filled with a gas in which the speed of sound is constant. Hence show that the number of...
  19. 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...
  20. S

    I Macroscopic versus microscopic standing waves

    I have read the description of electrons as standing waves based on an analogy with a string vibrating at its natural frequencies: thus the different quantum levels are akin to the tones or harmonics of the string, right? So far, so good, but then I have seen contradictory complementary views...
  21. 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...
  22. C

    Mechanical energy in an harmonic wave and in normal modes

    I think I miss something about energy of a mechanical wave. In absence of dissipation the mechanical energy transported by an harmonic wave is constant. $$E=\frac{1}{2} A^2 \omega^2 m$$ But, while studying normal modes on a rope, I find that the mechanical energy of a normal mode (still...
  23. ashsully

    B Confusion with Waves

    Hi everyone. I'm currently studying waves in physics at the moment but I'm super confused and hoping someone could help me clear up some things. Firstly I'll post what I think it correct (I know it's wrong) and hopefully someone could pick up exactly where I am getting confused. Waves are a...
  24. J

    A Reducing standing waves with phase randomization

    Will constantly randomizing the phase of an audio signal, say a speaker in the corner of a square room, reduce standing waves (i.e. room modes) in the room? For example if you wanted to create a diffuse field in a small (i.e. no standing wave interference patterns) at low frequencies.
  25. steven george

    I Frequencies of standing waves in a straw

    I am a physics teacher and I my class is currently studying sound waves. I had my class make some noise makers with straws as shown here. We measured the frequencies coming from the straws and they seem to act like a pipe open at...
  26. hiver

    Finding the value of g using 2nd Harmonic Frequency

    Homework Statement As the captain of the scientific team sent to Planet Physics, one of your tasks is to measure g. You have a long, thin wire labeled 1.80 g/m and a 1.30 kg weight. You have your accurate space cadet chronometer but, unfortunately, you seem to have forgotten a meter stick...
  27. V

    Find the Minimum Length of a Vibrating String

    Homework Statement the equation of a stationary wave produced on a string whose both ends are fixed is given by y= [0.6sin(pi/10)x]cos(600pi)t what could be the smallest length of string? Homework Equations k=2pi/wavelength The Attempt at a Solution i got the wavelength to be 20 but don't...
  28. F

    Reflection of Waves and Formation of Standing Waves

    I have three doubts in regard to waves on a string which I will try to make as clear as possible. For this purpose, I have considered a general wave: $$y_i=y_0\sin(\omega t - kx)$$ (1) If a wave pulse: $$y = y_0 e^{\frac{-1}{T^2} \left(t-\frac xv \right)^2}$$ is incident against a rigid...
  29. N

    No mass for mass per unit length

    Homework Statement A ski gondola is connected to the top of a hill by a steel cable of length L and radius R . As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took T seconds for the pulse to return. What is...
  30. Mnemonic

    Goniometers and Standing Waves

    Homework Statement Initially your receiver is positioned at a distance of 8.4 cm from the goniometer and recording a maximum intensity. You move it through 10 minimums in the intensity and then stop at the next maximum intensity. The receiver is now a distance of 27.3 cm from the goniometer...