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.
Hi everyone,
I'm curious if standing waves must be sinusoidal or if they can also be non-sinusoidal. Can anyone point me to videos or simulations of non-sinusoidal standing waves in action?
Thanks!
Good evening,
I'm working on the following problem and running into a little trouble:
Part (a) and (b) were super easy, but I have a question on part (c).
I'm trying to graph the total wave at ##t=0##, and it says I should get something that looks like this:
My graph doesn't even...
I think I understand that points P and R are pi radians out of phase - reaching their max/min at the same time.
But are P and Q in anti phase?
What is antiphase exactly - is it when they are 180deg out of phase - or is it when they are anything other than totally in phase? I seem to find...
During our classes, we haven't discussed the situation of a tube closed at both ends. But, assuming the position of the nodes and antinodes, I think it's a case similar to the one where the tube is open at both ends, so I think that f = v/λ = nv/(2L). Using the numeric data, my frequency would...
Variables:
Dependent: Vibrational frequency of violin string (Measured using mobile tuning app)
Independent: Temperature in which string is plucked (Measured using infrared thermometer)
Controlled: Violin String, Tension of violin string, Length of violin string, Method of plucking...
The question is to explain the equation of motion of the red ball. The string is massless and a small ball of mass m is attached to the string halfway. I just assumed the mass of the string is the same as the mass of the ball and explained the equation A cos(Wt) by defining the terms. I'm not...
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...
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?
Points A b AND C are shown in first diagram
Im confused about question three... I feel like its related to wave length but the fractions are throwing me off.
Hello everyone.
I'm having some trouble understanding waves. Particularly standing waves in an open tube.
So we have an open tube, someone blowing air into it creating a first harmonic and we have particles oscillating back and forth. The particles oscillating pressurize where the air...
The immediate thing i did here is
## \Delta \varphi = k(\Delta x) ##
Interesting enough for a topic, if you use this equation you end up wrong like me, the answer is not D.
Not sure what is the problem.
If the standing waves for beats are the longitudinal ones. what are the basis for differentiating from transverse.The beats have also nodes, there is a difference such from the transverse waves.Do they too have harmonics? the tones produced in case of beats also depends upon whether for...
Hi guys,
so I am struggling on the Standing Waves concept. I understand that these are waves that move in place but I don't know how to attempt this problem. Can someone set me on the right track?
If one speaker is placed facing another speaker with the inverted phase and we reproduce an equal frequency in both, what happened?
Did the sound completely cancel out or would a standing wave be created as if it were in phase?
Is this animation valid for sound waves...
I’ve seen the description of electrons around an atom as existing as standing waves with different harmonics corresponding to different energy levels.
The atom is evidently 3-dimensional, and the wave function of an electron must also be in terms if 3 spatial coordinates.
What mathematical...
Part C.
First of all, I am not entirely sure what the problem means by "loops." (I see the loops, duh ;)) but I am not sure what quantity they represent. I am guessing it means harmonics, in which case M would have to be lessened to make a greater wavelength. This is because the extension of...
I learned that standing waves form when the incident wave's frequency is equivalent to the reflected wave's frequency. But I also learned that according to Newton's 3rd law, when a wave hits a boundary, the reflected wave continues to travel in the opposite direction but has equal frequency and...
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 does...
Hello forum,
I am wondering why the higher order (higher harmonics) standing waves developed on a string under tension generated by an oscillating mechanical vibrator (set at the same amplitude but with variable frequency) have lower amplitude when compared to the lower harmonics (the...
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...
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...
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...
Homework Statement
In a resonance tube experiment, a closed organ pipe of length 120 cm resonates ,when tuned with a tuning fork of length 120cm resonates,when tuned with a tuning fork of length 340 hz.If water is poured into the pipe ,then (speed of sound in air=340 ms^-1)
(A) minimum length...
Hello,
The guitar is a stringed instrument with six strings of equal length but different linear mass density. Fretting is about shortening the length of a string which causes the fundamental mode and higher modes to have higher resonant frequencies.
When a guitar string is plucked (by hand...
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 playing...
Homework Statement
Homework Equations
Harmonics equations
The Attempt at a Solution
So, I got (A), which is the answer key is correct, but I'm not sure whether my reasoning is right or not. Would this be considered a closed-end air column question? Anyways, according to the length-wavelength...
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...
1. The problem statement, all variables, and given/known data
Consider a two-loop standing wave on a string. If we increase the tension without changing the frequency, what kind of standing wave can we obtain?
(a) one-loop (b) three-loop
Homework Equations
Velocity = square root of(T/U)...
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...
In a sound wave, air is being compressed and decompressed. If sound is reflected at the end, then to create a standing wave the compressed layer of air coming back must coincide with another compressed layer of air going forward.
If that's the case, how can the compressed airs continue to...
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...
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...
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...
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...
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...
Homework Statement
String A is stretched between two clamps separated by distance L. String B, with the same linear density and under the same tension as string A. String B is stretched between two clamps separated by distance 4L. Consider the first eight harmonics of string B. For which of...
Hello,
I am aware that there are specific oscillatory patterns than can form on on a string. These patterns are called normal modes and represent standing waves. Each standing wave has an associated frequency f which indicates the speed at which the string's points are moving up and down...
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...
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...
Homework Statement
So in our report we have to explain why these formulas give the same answer theoretically.
We have for an example measured these numbers:
Freq.: 16,37 Hz
L: 1m
m: 0.007 kg
T ≈ 1 N
λ=1/1=1
Homework Equations
v=ƒ*λ=√T/(m/L)
The Attempt at a Solution
The problem is that I...
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...
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...
Hi there,
I am reading a book regarding fundamental atomic physics, in which it introduces one kind of electronic scattering called Kapitsa–Dirac effect. I read the some introduction in wiki https://en.wikipedia.org/wiki/Kapitsa%E2%80%93Dirac_effect, and it states that the effect was first...
Homework Statement
The ends of a stretched wire of length L are fixed at x=0 and x=L. In one experiment, the displacement of the wire is given by ##y=A\sin\left(\frac{\pi x}{L}\right)\sin(\omega t)## and its energy is ##E_1##. In another experiment, the displacement of wire is given by...
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...