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

[sophiecentaur]

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'?

 

[jsmith613]

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

 

[sophiecentaur]

Ah yes.
The resultant would be the same in amplitude over all distances 2A Cos(1 degree). A very 'long standing wave'.

 

[jsmith613]

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

 

[sophiecentaur]

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.

 

[jsmith613]

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?

 

[sophiecentaur]

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.