Interference at a single wavelength

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Homework Help Overview

The discussion revolves around the concept of interference at a single frequency, particularly focusing on the conditions under which interference occurs between waves. The original poster questions whether interference implies that the waves are completely in phase and explores the implications of waves that are out of phase.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to clarify the meaning of interference at a single frequency and whether it requires the waves to be in phase. They also inquire about the interaction of waves that are out of phase by half a wavelength.

Discussion Status

The discussion includes attempts to clarify the nature of interference and the conditions necessary for constructive and destructive interference. Some participants provide insights into the relationship between frequency and amplitude in the context of interference.

Contextual Notes

Participants are exploring the definitions and implications of interference, particularly in relation to phase and frequency, without reaching a definitive consensus on all points raised.

physical101
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Homework Statement



I have a question relating to the interference at a single frequency? Does this statement mean that the intereference has occurred between two waves which are completely in phase? I also have a question regarding if two waves which are not in phase but do not cause complete destruction or construction ie they are out of phase by a 1/2 a wavelength for example would the still interact and produce a new wavelength?

Homework Equations





The Attempt at a Solution

 
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Welcome to PF!

Hi physical101! Welcome to PF! :smile:
physical101 said:
I have a question relating to the interference at a single frequency? Does this statement mean that the intereference has occurred between two waves which are completely in phase? I also have a question regarding if two waves which are not in phase but do not cause complete destruction or construction ie they are out of phase by a 1/2 a wavelength for example would the still interact and produce a new wavelength?

I suspect you're thinking of beats, for example in sound waves, when two nearby frequencies are added.

No, a single frequency stays at that frequency.

Asinωt + Bsin(ωt+φ) = (A + Bcosφ)sinωt + Bsinφcosωt,

which is a multiple of sin(ωt+ψ), where tanψ = Bsinφ/(A + Bcosφ) :wink:
 
so would I be correct in thinking that when a journal/literature states that intereference has occurred at a single frequency that the resultant wave would be increased in amplitude due to total constructive intereference? What I am trying to clarify is that when they state that interference has occurred at a single frequency that the interefering waves were of the same frequency to begin with? Sorry if I am not making much sense
 
physical101 said:
so would I be correct in thinking that when a journal/literature states that intereference has occurred at a single frequency that the resultant wave would be increased in amplitude due to total constructive intereference? What I am trying to clarify is that when they state that interference has occurred at a single frequency that the interefering waves were of the same frequency to begin with? Sorry if I am not making much sense

Hi physical101! :wink:

No, you're making complete sense: that's exactly correct.

Constructive interference starts with the same frequency it finishes with (and so does destructive interference). Only the amplitude (and maybe the phase) changes. :smile:
 

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