What are the properties of a wave?

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SUMMARY

The discussion centers on the properties of waves, specifically addressing the concept of "dark fringes" resulting from destructive interference. A wave is defined as a disturbance that propagates through a medium, described mathematically by the wave equation. The conversation emphasizes that all wave behaviors, including patterns of interference, can be derived from this mathematical framework. The participants highlight the importance of understanding the underlying mathematics to grasp wave phenomena fully.

PREREQUISITES
  • Understanding of the wave equation and its mathematical formulations
  • Basic knowledge of wave interference, including constructive and destructive interference
  • Familiarity with different types of waves, such as sound waves and electromagnetic waves
  • Concept of wave propagation and its effects in various media
NEXT STEPS
  • Study the mathematical wave equation and its solutions, including sinusoidal functions
  • Explore the principles of wave interference and its applications in physics
  • Investigate different types of waves, focusing on sound and electromagnetic waves
  • Learn about practical applications of wave behavior in technology, such as in acoustics and optics
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Students of physics, educators teaching wave mechanics, and anyone interested in the mathematical foundations of wave phenomena will benefit from this discussion.

Arup Biswas
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Yaahh...After deploying all my grey matters on interference I just came to a conclusion that "What is wave?" Do we have the right pictorial diagram of a wave? But please don't through the the 'ficticious' thought I like too much, just answer "Why we get a dark 'fringe'? 'Fringe'?" Shouldn't we get a pattern like the the dark 'point' or 'line'? And if you imagined the question right, should also understand what the patter like I'm talking to! And again, I put in the Science Fiction class so not necessarily it has a logic may be foolish but worthy [emoji6][emoji6]
 
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Arup Biswas said:
just answer "Why we get a dark 'fringe'?
Because of destructive interference
'Fringe'?" Shouldn't we get a pattern like the the dark 'point' or 'line'
depends on the source of the interfering waves.
 
Arup Biswas said:
Yaahh...After deploying all my grey matters on interference I just came to a conclusion that "What is wave?" Do we have the right pictorial diagram of a wave? But please don't through the the 'ficticious' thought I like too much, just answer "Why we get a dark 'fringe'? 'Fringe'?" Shouldn't we get a pattern like the the dark 'point' or 'line'? And if you imagined the question right, should also understand what the patter like I'm talking to! And again, I put in the Science Fiction class so not necessarily it has a logic may be foolish but worthy [emoji6][emoji6]

Your post his highly confusing and very difficult to follow. It is hard to distill exactly what you are asking.

Due to that, I will tackle what you wrote in the title of the thread. The answer to "What is actually wave?" (sic) is actually quite simple. It is any system that can be written down in the form of the mathematical wave equation.

Everything else, such as "dark fringes", etc...etc., are consequences of this mathematical description, and can be derived from it. So any system that can satisfy this mathematical form can possibly exhibits all those wave behaviors.

This is why in physics, practically every single concepts and ideas have strong underlying mathematical description. It isn't just words. Rather, those words are accompanied by mathematical formulations. Each time we utter the words such as "Oh, it is a wave", we all know and are aware of what that entails, and all the mathematical and physical rules and consequences.

Zz.
 
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I would agree, please put more thought and effort into writing the questions. It is exceedingly hard to understand what is being asked.
 
There are different types of waves - we usually visualize waves as what we see happen in water, but waves in air or emf waves are fluctuations in pressure, or in magnetic fields. Any non-static system that has something alternating in it = waves. You can get all kinds of different patterns when adding waves together - can get them to cancel one another out, or reinforce one another - seems like there are an infinite number of different combinations and patterns you could create - so sure, why not, you could crash two waves together and create a line between them, or funnel them into some sort of a point I suppose?
 
Arup Biswas said:
Do we have the right pictorial diagram of a wave?

Yes. Compare the pictorial diagram with a wave on the open sea.
 
Arup Biswas said:
Yaahh...After deploying all my grey matters on interference I just came to a conclusion that "What is wave?" Do we have the right pictorial diagram of a wave? But please don't through the the 'ficticious' thought I like too much, just answer "Why we get a dark 'fringe'? 'Fringe'?" Shouldn't we get a pattern like the the dark 'point' or 'line'? And if you imagined the question right, should also understand what the patter like I'm talking to! And again, I put in the Science Fiction class so not necessarily it has a logic may be foolish but worthy [emoji6][emoji6]
Hi. I can tell that English is not your first language but well done for trying.
Here is a simple, general description of what we mean by a 'Wave"
A wave describes how a disturbance of any kind propagates through a medium and this is NEVER instantaneous. There is always some delay between a change in one thing (say the blip of a loudspeaker cone) and what happens to your ear drum. The pulse of pressure travels through the air from molecule to molecule and we describe that as a wave. A continuous wave can be produced by a loudspeaker or a radio transmitter etc etc. and the there can be several waves traveling to your ear. If they are at the same frequency then they can augment or cancel at the location of your ear.
This effect of addition and cancellation is general for all waves. Once it has been launched, the energy is never 'lost' but redirected from some regions (nulls) to others (maxima), which produces "fringes" of loud and quiet , light and dark, good and bad TV reception etc.
What else you need will depend on your level of Science of Maths understanding.
 
A wave is any solution to the wave equation
##\frac{\partial^2 u}{\partial t^2} = c^2 \nabla^2 u##
(Sometimes a generalized wave equation might be used)
Some solutions are
##\sin(k.x-\omega t), \cos(k.x-\omega t), e^{i(k.x-\omega t)}##. Since the (homogeneous) wave equation is linear, any sum of solutions to the wave equation is another solution. So you can get fairly complicated waves. You can have propagating waves or standing waves or something in between.
 

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