Wave sources vibrating out of phase (destructive/constructive)

[kurt1992]

Homework Statement

If the phase of vibrating sources was changed so that they were vibrating completely out of phase, what effect would this have on an interference pattern?

Homework Equations

n/a

The Attempt at a Solution

This question undermines my understanding of interference, 2 sources in phase of equal wavelength will cause both destructive and constructive interference, the pattern consists of a constructive band m=0, 2 destructive bands n=±1, 2 constructive bands m=±1 etc.

I thought that constructive/destructive interference all depended on the existence of a point of distance x from each source (the waves could overlap or be shifted by ∏/2 rads along the x axis)

My question to you, physics people is: is this question viable, how will the interference pattern change if the sources are completely out of phase.

 

[STEMucator]

Homework Statement

If the phase of vibrating sources was changed so that they were vibrating completely out of phase, what effect would this have on an interference pattern?

Homework Equations

n/a

The Attempt at a Solution

This question undermines my understanding of interference, 2 sources in phase of equal wavelength will cause both destructive and constructive interference, the pattern consists of a constructive band m=0, 2 destructive bands n=±1, 2 constructive bands m=±1 etc.

I thought that constructive/destructive interference all depended on the existence of a point of distance x from each source (the waves could overlap or be shifted by ∏/2 rads along the x axis)

My question to you, physics people is: is this question viable, how will the interference pattern change if the sources are completely out of phase.

Suppose you have 2 sources in phase. They create an interference pattern of fringes on a screen some distance away from the slits.

If you were to cause these sources to vibrate out of phase, I believe nodes and antinodes would switch their roles.

 

[kurt1992]

I had a gut feeling that the nodes and anti nodes would reverse roles, seems to agree with the whole idea in math than an inverse cause will have an inverse effect.

If anyone has any more info why the nodes and anti-nodes switch roles please enlighten me :)

 

[STEMucator]

I had a gut feeling that the nodes and anti nodes would reverse roles, seems to agree with the whole idea in math than an inverse cause will have an inverse effect.

If anyone has any more info why the nodes and anti-nodes switch roles please enlighten me :)

I believe it has to do with the path differences.

If waves are in phase, then the path differences are such that the waves reach the screen with crests superimposing crests and troughs superimposing troughs. This happens when the periods of each wave are equal or the paths themselves differ by a whole number multiple of the wavelength (λ, 2λ, 3λ, ...).

Now make these waves out of phase. Then half of the waves will travel half a wavelength farther than the rest. So the path difference will be 0.5λ, 1.5λ, 2.5λ, ...

 

[HalfLostAndSearching]

I would like to clarify that the question is indeed viable. When two wave sources vibrate completely out of phase, it means that their vibrations are exactly opposite of each other. This results in a complete cancellation of the waves, leading to a net amplitude of zero. Therefore, there would be no interference pattern observed at all. This is because the constructive and destructive interference rely on the overlapping of waves to create the pattern. If the waves are completely out of phase, there is no overlapping and hence no pattern. This concept is known as destructive interference.

On the other hand, if the two sources were vibrating in phase, the resulting interference pattern would be the same as if only one source were present. This is known as constructive interference. The pattern would consist of alternating bands of constructive and destructive interference, as you have described.

In summary, changing the phase of vibrating sources to be completely out of phase would result in no interference pattern, as the waves would cancel each other out. This is a fundamental concept in wave interference and is important to understand in various fields of science, such as optics and acoustics.