Why must traveling waves have the same amplitude to form a standing wave?Why is a particular wavelength...
Playing ONE triplet (not three)
What happens with multiple copies of Humility and Glorious Anthem on the battlefield?
What has been your most complicated TikZ drawing?
What is the definition of "Natural Selection"?
Can infringement of a trademark be pursued for using a company's name in a sentence?
Is "history" a male-biased word ("his+story")?
What is the blue range indicating on this manifold pressure gauge?
It's a yearly task, alright
Why would a jet engine that runs at temps excess of 2000°C burn when it crashes?
Are there situations where a child is permitted to refer to their parent by their first name?
Best mythical creature to use as livestock?
What is the dot in “1.2.4."
What wound would be of little consequence to a biped but terrible for a quadruped?
Unreachable code, but reachable with exception
what does the apostrophe mean in this notation?
Best approach to update all entries in a list that is paginated?
Question about partial fractions with irreducible quadratic factors
What Happens when Passenger Refuses to Fly Boeing 737 Max?
Is a lawful good "antagonist" effective?
Force user to remove USB token
If the Captain's screens are out, does he switch seats with the co-pilot?
Do f-stop and exposure time perfectly cancel?
Can you reject a postdoc offer after the PI has paid a large sum for flights/accommodation for your visit?
When is a batch class instantiated when you schedule it?
Why must traveling waves have the same amplitude to form a standing wave?
Why is a particular wavelength favored by transmission through a thin film?Why is the phase of reflected wave during formation of standing waves 180 degrees?Molecular orbital theoryHow are standing waves a result of constructive and destructive interferences?Constructive and destructive interferenceThe relationship between the standing wave energy and its harmonicConceptual doubt regarding Standing Waves, in particular constructing a Standing Wave after t=T/2 secondsWhy are standing waves produced in an open organ pipe if the medium is same after all?Standing waves in antenna: why is the current wave symmetric with respect to the centre?On Superposition In Diffraction
$begingroup$
I understand the reason for which the wavelengths of the incident and reflected waves must be equal: otherwise, the interference at any fixed position would be constructive at some instants and destructive at others. But why can't two waves of differing amplitude produce a standing wave?
waves
asked 2 hours ago
Julia KimJulia Kim
274
$endgroup$
add a comment |
$begingroup$
I understand the reason for which the wavelengths of the incident and reflected waves must be equal: otherwise, the interference at any fixed position would be constructive at some instants and destructive at others. But why can't two waves of differing amplitude produce a standing wave?
waves
asked 2 hours ago
Julia KimJulia Kim
274
$endgroup$
add a comment |
$begingroup$
I understand the reason for which the wavelengths of the incident and reflected waves must be equal: otherwise, the interference at any fixed position would be constructive at some instants and destructive at others. But why can't two waves of differing amplitude produce a standing wave?
waves
asked 2 hours ago
Julia KimJulia Kim
274
$endgroup$
I understand the reason for which the wavelengths of the incident and reflected waves must be equal: otherwise, the interference at any fixed position would be constructive at some instants and destructive at others. But why can't two waves of differing amplitude produce a standing wave?
waves
waves
asked 2 hours ago
Julia KimJulia Kim
274
asked 2 hours ago
Julia KimJulia Kim
274
asked 2 hours ago
Julia KimJulia Kim
274
asked 2 hours ago
Julia KimJulia Kim
274
asked 2 hours ago
Julia KimJulia Kim
274
274
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
If the travelling waves have the same amplitude then the net rate of transfer of energy at any point is zero and there are stationary positions where the standing wave has zero amplitude - nodes.
In this animation taken from Acoustics and Vibration Animations the amplitude of the reflected wave is the same as that of the incident wave.
If the travelling waves are of unequal amplitude then there is a net transfer of energy.
If the amplitudes of the two traveling waves are $A$ and $B$ with $A>B$ then you can think of the superposition of the two travelling waves as being the sum of a standing wave formed by two travelling waves of amplitude $B$ and a travelling wave of amplitude $A-B$.
In this animation the amplitude of the left travelling (incident) wave is larger than that of the right travelling (reflected) wave and so there is a net transfer of energy from left to right.
If you look carefully using a vertical ruler as a marker you will observe positions of maximum displacement and positions of minimum (but not zero) displacement.
The graph bottom left of this video shows this maximum and minimum displacement by overlapping the wave profiles as time progresses.
answered 56 mins ago
FarcherFarcher
50.8k338106
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "151"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphysics.stackexchange.com%2fquestions%2f466359%2fwhy-must-traveling-waves-have-the-same-amplitude-to-form-a-standing-wave%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
If the travelling waves have the same amplitude then the net rate of transfer of energy at any point is zero and there are stationary positions where the standing wave has zero amplitude - nodes.
In this animation taken from Acoustics and Vibration Animations the amplitude of the reflected wave is the same as that of the incident wave.
If the travelling waves are of unequal amplitude then there is a net transfer of energy.
If the amplitudes of the two traveling waves are $A$ and $B$ with $A>B$ then you can think of the superposition of the two travelling waves as being the sum of a standing wave formed by two travelling waves of amplitude $B$ and a travelling wave of amplitude $A-B$.
In this animation the amplitude of the left travelling (incident) wave is larger than that of the right travelling (reflected) wave and so there is a net transfer of energy from left to right.
If you look carefully using a vertical ruler as a marker you will observe positions of maximum displacement and positions of minimum (but not zero) displacement.
The graph bottom left of this video shows this maximum and minimum displacement by overlapping the wave profiles as time progresses.
answered 56 mins ago
FarcherFarcher
50.8k338106
$endgroup$
add a comment |
$begingroup$
If the travelling waves have the same amplitude then the net rate of transfer of energy at any point is zero and there are stationary positions where the standing wave has zero amplitude - nodes.
In this animation taken from Acoustics and Vibration Animations the amplitude of the reflected wave is the same as that of the incident wave.
If the travelling waves are of unequal amplitude then there is a net transfer of energy.
If the amplitudes of the two traveling waves are $A$ and $B$ with $A>B$ then you can think of the superposition of the two travelling waves as being the sum of a standing wave formed by two travelling waves of amplitude $B$ and a travelling wave of amplitude $A-B$.
In this animation the amplitude of the left travelling (incident) wave is larger than that of the right travelling (reflected) wave and so there is a net transfer of energy from left to right.
If you look carefully using a vertical ruler as a marker you will observe positions of maximum displacement and positions of minimum (but not zero) displacement.
The graph bottom left of this video shows this maximum and minimum displacement by overlapping the wave profiles as time progresses.
answered 56 mins ago
FarcherFarcher
50.8k338106
$endgroup$
add a comment |
$begingroup$
If the travelling waves have the same amplitude then the net rate of transfer of energy at any point is zero and there are stationary positions where the standing wave has zero amplitude - nodes.
In this animation taken from Acoustics and Vibration Animations the amplitude of the reflected wave is the same as that of the incident wave.
If the travelling waves are of unequal amplitude then there is a net transfer of energy.
If the amplitudes of the two traveling waves are $A$ and $B$ with $A>B$ then you can think of the superposition of the two travelling waves as being the sum of a standing wave formed by two travelling waves of amplitude $B$ and a travelling wave of amplitude $A-B$.
In this animation the amplitude of the left travelling (incident) wave is larger than that of the right travelling (reflected) wave and so there is a net transfer of energy from left to right.
If you look carefully using a vertical ruler as a marker you will observe positions of maximum displacement and positions of minimum (but not zero) displacement.
The graph bottom left of this video shows this maximum and minimum displacement by overlapping the wave profiles as time progresses.
answered 56 mins ago
FarcherFarcher
50.8k338106
$endgroup$
If the travelling waves have the same amplitude then the net rate of transfer of energy at any point is zero and there are stationary positions where the standing wave has zero amplitude - nodes.
In this animation taken from Acoustics and Vibration Animations the amplitude of the reflected wave is the same as that of the incident wave.
If the travelling waves are of unequal amplitude then there is a net transfer of energy.
If the amplitudes of the two traveling waves are $A$ and $B$ with $A>B$ then you can think of the superposition of the two travelling waves as being the sum of a standing wave formed by two travelling waves of amplitude $B$ and a travelling wave of amplitude $A-B$.
In this animation the amplitude of the left travelling (incident) wave is larger than that of the right travelling (reflected) wave and so there is a net transfer of energy from left to right.
If you look carefully using a vertical ruler as a marker you will observe positions of maximum displacement and positions of minimum (but not zero) displacement.
The graph bottom left of this video shows this maximum and minimum displacement by overlapping the wave profiles as time progresses.
answered 56 mins ago
FarcherFarcher
50.8k338106
edited 45 mins ago
answered 56 mins ago
FarcherFarcher
50.8k338106
answered 56 mins ago
FarcherFarcher
50.8k338106
answered 56 mins ago
FarcherFarcher
50.8k338106
50.8k338106
add a comment |
add a comment |
Thanks for contributing an answer to Physics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphysics.stackexchange.com%2fquestions%2f466359%2fwhy-must-traveling-waves-have-the-same-amplitude-to-form-a-standing-wave%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
