Interference at a single wavelength

In summary: in summary, interference has occurred at a single frequency, the resultant wave will be increased in amplitude due to total constructive interference.
  • #1
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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  • #2
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:
 
  • #3
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
 
  • #4
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:
 

Related to Interference at a single wavelength

1. What is interference at a single wavelength?

Interference at a single wavelength occurs when two or more waves of the same wavelength meet and interact with each other, resulting in a new wave with a different amplitude and direction of travel.

2. What causes interference at a single wavelength?

Interference at a single wavelength is caused by the superposition of two or more waves that are in phase or out of phase with each other. This can occur when the waves originate from the same source or from different sources.

3. How does interference at a single wavelength affect the amplitude of the resulting wave?

The amplitude of the resulting wave from interference at a single wavelength can either increase or decrease, depending on whether the waves are in phase or out of phase. When the waves are in phase, the amplitude will increase, and when they are out of phase, the amplitude will decrease.

4. What is the difference between constructive and destructive interference at a single wavelength?

Constructive interference occurs when two waves are in phase and their amplitudes add together, resulting in a wave with a larger amplitude. Destructive interference occurs when two waves are out of phase and their amplitudes cancel out, resulting in a wave with a smaller amplitude.

5. How is interference at a single wavelength used in practical applications?

Interference at a single wavelength is used in various applications, such as in fiber optics communication, where it allows for the transmission of multiple signals through a single fiber. It is also used in interferometers, which are devices used to measure small changes in distance or wavelength. Additionally, interference at a single wavelength is used in music and sound production to create different effects and tones.

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