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

In summary, standing waves are produced by the superposition of a propagating wave and a reflected wave, resulting in a wave of zero propagation. The nodes, where there is zero displacement, are fixed points due to the cancellation of the two waves. Antinodes, where there is maximum displacement, are caused by the constructive interference of the two waves. Standing waves can be immediately created in certain arrangements, and can be identified through a suitable probe. Harmonics are multiples of the fundamental frequency and can be observed in practical resonating systems, although they may not align exactly with the harmonic frequencies due to end effects. Multiple resonances can occur simultaneously, contributing to the timbre of musical instruments.
  • #71
This has got to be just another misunderstanding. the forward and reflected wave vary in relative phase from in-phase to anti-phase as you look at different points along the standing wave. This is why the resultant amplitudes vary from zero to double value.
I could suggest thinking of two phasors, their relative angles steadily changing (in opposite senses) as you look at points along the 'string'.
If you change the phase of one of the waves - say by using a delay at the reflection, then everything is the same except for the precise places where the anti and in phase conditions apply.

This thread has discussed many scenarios and I have assumed that the main discussion is about the formation of a standing wave when a reflection occurs - i.e. two waves of the same frequency are traveling towards each other. In that situation, my statement must be true, surely? In which way is it not?
Do you object to my use of the term 'interference pattern'?
 
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  • #72
sophiecentaur said:
This thread has discussed many scenarios and I have assumed that the main discussion is about the formation of a standing wave when a reflection occurs - i.e. two waves of the same frequency are traveling towards each other. In that situation, my statement must be true, surely? In which way is it not?
Do you object to my use of the term 'interference pattern'?

I think the confusion may be as follows:
- the main topic is about standing waves BUT we have been side-tracked. It may be that the confusion is between two waves that are moving in the same direction and are 1 degree out of phase (and remain this way) v.s waves that are traveling in opposite directions
 
  • #73
Ah yes.
The resultant would be the same in amplitude over all distances 2A Cos(1 degree). A very 'long standing wave'.
 
  • #74
sophiecentaur said:
Ah yes.
The resultant would be the same in amplitude over all distances 2A Cos(1 degree). A very 'long standing wave'.

Now even I am confused!
If we have the standing wave, they would only be 1 degree out of phase at one point..

I was referring to two waves traveling in the same direction and superimposing where the phase difference was 1 degree.
Then would deconstructive interference occur or would it be defined as constructive
 
  • #75
Could you tell the difference by looking?
The con and des terms are only approximate, aren't they? Certainly only useful for arm waving or, sometimes, for finding a minimum / null in interferometry etc.. What is really relevant is the actual value.
If they are from non-coincident sources you would, in fact, be producing a two slits interference pattern.
 
  • #76
sophiecentaur said:
Could you tell the difference by looking?
The con and des terms are only approximate, aren't they? Certainly only useful for arm waving or, sometimes, for finding a minimum / null in interferometry etc.. What is really relevant is the actual value.
If they are from non-coincident sources you would, in fact, be producing a two slits interference pattern.

surely in an ideal situation (such as an exam question - which is one of the things I am working towards) they may ask the basic question
"Wave A and B are 10 degrees out of phase. When they superimpose would we get a constructive or deconsrtuctive interferance pattern. Explain"

In this case would the following answer suffice
"They would interfere constuctivley as the total displacement is greater than that of both individual waves".



Maybe i was confusing myself by using the value 1 degree. It would actually ONLY make sense if deconstructive intferferene took place at 180 degrees out of phase, right?

Reason being that this is the only stage where maximum displacement is less than that of either / both waves individually?
 
  • #77
Any decent Science exam question would really not concern itself with such semantic ideas. If it were to ask you what the value of the resultant was, you should be able to work it out with a simple vector triangle and get full marks. If you were at too low a level of knowledge then an appropriate question wouldn't introduce the phase value.
You seem determined to keep this topic at a 'conversational' level when, as I have remarked twice already, the Maths say it all and, at your level, that's what would count. It really is the only way forward. I have never come across any question on the lines of your proposed one - for a start, what could be the marking scheme?
All one can say, conversationally, is that the maximum is for zero phase difference and the deepest part of a null is when they are in antiphase - but we all knew that even before this thread started.
 
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<h2>1. What is the fundamental principle of standing waves?</h2><p>The fundamental principle of standing waves is that when two waves of the same frequency and amplitude travel in opposite directions through a medium, they interfere with each other and create a pattern of nodes (points of no displacement) and antinodes (points of maximum displacement).</p><h2>2. How does phase play a role in standing waves?</h2><p>Phase refers to the position of a wave at a specific point in time. In standing waves, the phase of the two interfering waves must be the same in order for the pattern of nodes and antinodes to form. This means that the two waves must have the same starting point and travel in opposite directions with the same frequency and amplitude.</p><h2>3. Can standing waves occur in any medium?</h2><p>Yes, standing waves can occur in any medium where waves can propagate, such as air, water, or even solid objects. However, the medium must be able to support the necessary conditions for standing waves, such as the ability for waves to reflect and interfere with each other.</p><h2>4. How is the wavelength of a standing wave determined?</h2><p>The wavelength of a standing wave is determined by the distance between two consecutive nodes or antinodes. This distance is equal to half of the wavelength of the individual waves that are interfering to create the standing wave.</p><h2>5. What are some practical applications of standing waves?</h2><p>Standing waves have many practical applications, including in musical instruments such as stringed instruments and wind instruments. They are also used in medical imaging techniques like ultrasound, and in telecommunications for transmitting and receiving signals. Additionally, standing waves are important in understanding the behavior of electromagnetic waves, which are used in technologies like radio and television broadcasting.</p>

1. What is the fundamental principle of standing waves?

The fundamental principle of standing waves is that when two waves of the same frequency and amplitude travel in opposite directions through a medium, they interfere with each other and create a pattern of nodes (points of no displacement) and antinodes (points of maximum displacement).

2. How does phase play a role in standing waves?

Phase refers to the position of a wave at a specific point in time. In standing waves, the phase of the two interfering waves must be the same in order for the pattern of nodes and antinodes to form. This means that the two waves must have the same starting point and travel in opposite directions with the same frequency and amplitude.

3. Can standing waves occur in any medium?

Yes, standing waves can occur in any medium where waves can propagate, such as air, water, or even solid objects. However, the medium must be able to support the necessary conditions for standing waves, such as the ability for waves to reflect and interfere with each other.

4. How is the wavelength of a standing wave determined?

The wavelength of a standing wave is determined by the distance between two consecutive nodes or antinodes. This distance is equal to half of the wavelength of the individual waves that are interfering to create the standing wave.

5. What are some practical applications of standing waves?

Standing waves have many practical applications, including in musical instruments such as stringed instruments and wind instruments. They are also used in medical imaging techniques like ultrasound, and in telecommunications for transmitting and receiving signals. Additionally, standing waves are important in understanding the behavior of electromagnetic waves, which are used in technologies like radio and television broadcasting.

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