Interference at a single wavelength

[physical101]

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

 

[tiny-tim]

Welcome to PF!

Hi physical101! Welcome to PF!

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)

 

[physical101]

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

 

[tiny-tim]

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!

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.