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, ...