What distinguishes plane waves from wave packets in physics?

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    Plane Wave Wave packet
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Discussion Overview

The discussion centers on the distinctions between plane waves and wave packets in physics, exploring their definitions, characteristics, and the processes through which they are produced and utilized. It encompasses theoretical considerations and conceptual clarifications.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants note that plane waves are idealizations with infinite extent, while wave packets are more realistic and limited in extent.
  • It is proposed that a wave packet consists of a range of frequencies around a nominal frequency, whereas a continuous wave is characterized by a single frequency.
  • Questions are raised regarding the definition of plane waves and why they are considered infinite in extent, with some arguing that modulation is necessary to localize a wave, which introduces additional frequencies.
  • One participant asserts that the term "plane" implies infinite extent, and mentions that plane waves can have non-periodic profiles, such as those used to model shock waves, which contain all possible frequencies when analyzed through Fourier integrals.
  • Another participant acknowledges the relationship between Fourier analysis and spatial truncation, suggesting it relates to diffraction at boundaries.

Areas of Agreement / Disagreement

Participants express differing views on the definitions and implications of plane waves and wave packets, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Definitions of terms such as "plane wave" and "wave packet" may vary, and the discussion highlights the dependence on these definitions. The implications of modulation and frequency content are also noted as areas of complexity.

gentsagree
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Generally speaking, what is the difference between these two? What I mean by that is: in what kind of different processes are these produced (and used in physics)?
 
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Plane wave has infinite extent and is an idealization that cannot actually occur in the theory. The wave packet is limited in extent and is more realistic description according to the theory.
 
A 'packet wave' will consist of a range of frequencies, around the nominal frequency. A continuous wave (sinusoid) will, in the limit, consist of just one frequency.
 
Why are plane waves said to be infinite in extent? Why can't a wave have one frequency without being infinite in its "domain"?
 
sigma_ said:
Why are plane waves said to be infinite in extent? Why can't a wave have one frequency without being infinite in its "domain"?

It's a matter of definition. If the wave doesn't extend to infinity, it must be 'modulated' to localise it. If you modulate a continuous sinusoid, you introduce other frequencies (sidebands).
 
sigma_ said:
Why are plane waves said to be infinite in extent? Why can't a wave have one frequency without being infinite in its "domain"?

Because in "plane wave" you have the adjective "plane", which is by its meaning infinite in extent.

Frequencies have nothing to do with "plane wave". There are plane waves that have non-periodic profile, like ones used to model shock wave - when analyzed into Fourier integral, all possible frequencies are present.
 
sophiecentaur said:
It's a matter of definition. If the wave doesn't extend to infinity, it must be 'modulated' to localise it. If you modulate a continuous sinusoid, you introduce other frequencies (sidebands).
Got it. Thanks
 
sigma_ said:
Got it. Thanks

Btw, that Fourier business works for spatial truncation too. That accounts for diffraction at a boundary.
 

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