Constructive Wave Interference: Can Two Waves Combine?

  • Context: Undergrad 
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Discussion Overview

The discussion revolves around the conditions for constructive wave interference, specifically whether two waves with the same frequency and wavelength can combine constructively even if they have different amplitudes. The scope includes theoretical considerations of wave behavior and interference patterns.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions if two waves with the same frequency and wavelength can combine constructively despite differing amplitudes.
  • Another participant expresses agreement with the possibility of constructive interference occurring under these conditions.
  • A different participant references their book, suggesting that constructive interference requires equal amplitude, frequency, and wavelength, but acknowledges the prompt reply from the previous participant.
  • Another participant challenges the idea that equal amplitude is necessary for constructive interference, stating that only equal amplitude is required for complete destructive interference.
  • A later reply suggests revisiting the mathematical formulation of wave addition to clarify the concept.

Areas of Agreement / Disagreement

Participants express differing views on whether equal amplitude is necessary for constructive interference, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Some assumptions about wave behavior and definitions of constructive versus destructive interference are not fully explored, and there are unresolved mathematical aspects related to wave addition.

Bashyboy
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Hi,

I was wondering if two waves, whom both have the same frequency and wave, could be combined together in a constructive interference way, even if they did not have the same amplitude?
 
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Sure, why not?
 
Well, my book made it seem as though constructive waves could be formed when the amplitude, frequency, and wavelength are the same. Thank you, by the way, for your prompt reply.
 
Bashyboy said:
Well, my book made it seem as though constructive waves could be formed when the amplitude, frequency, and wavelength are the same.
Well, the part about needing the same amplitude is not true for constructive interference. Now, to get completely destructive interference you do need the same amplitude, otherwise the out of phase waves would not completely cancel each other.
 
You can always remind yourself how this works by going back to the mathematics, e.g.,

\cos \omega t + 3 \cos \omega t = ?
 

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