Circular Wave Fronts Emitted by Two Wave Sources

[CentrifugalKing]

Homework Statement

https://session.masteringphysics.com/problemAsset/1383558/3/21.EX26.jpg

Make a table with rows labeled P, Q, and R and columns labeled r1, r2, Δr, and C/D. Fill in the table for points P, Q, and R, giving the distances as multiples of λ and indicating, with a C or a D, whether the interference at that point is constructive or destructive.

The Attempt at a Solution

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Okay, so I am not entirely sure I am doing this right. I have two attempts and used one. Can someone help me with this?

Here's my new answer R1 R2 Δr C/D
P 2λ 3λ λ C
Q 3λ 2λ λ D
R 2.5 3λ 0.5λ C

Would you say this is correct?

Sorry, the graph is out of place. idk how to forumat

 

[MikeN]

Surely the distances can only be integer multiples of λ if they lie on the circles?

 

[CentrifugalKing]

Surely the distances can only be integer multiples of λ if they lie on the circles?

I'm not quite sure what you are getting at here. Care to elaborate?

 

[MikeN]

Well, it looks like the circles are evenly spaced so presumably they are spaced at a distance of one wavelength from each other.

 

[CentrifugalKing]

Well, it looks like the circles are evenly spaced so presumably they are spaced at a distance of one wavelength from each other.

Oh yes I now understand. Yeah, they are spaced evenly. My problem is more along the lines of whether I counted right or not. I just wanted an outside confirmation

 

[MikeN]

There are a couple of errors, for example, R2 for P which is why I was making the point about integer multiples lying on the circles. You should also take another look at the C/D column.

 

[CentrifugalKing]

There are a couple of errors, for example, R2 for P which is why I was making the point about integer multiples lying on the circles. You should also take another look at the C/D column.

So should R2 be 3.5? Because that was what I initially thought but my answer choices lack a 3.5

Also, I'm not sure about anything regarding the C/D column

 

[MikeN]

Ah, looking at the diagram again, I think 3 might actually be correct. If you look at the first circle around 2 it seems to be around half the radius of 1 so I'd assume that the circles about 2 are 0.5λ, 1.5λ, 2.5λ... So you should probably take another look at R2 for Q.

 

[CentrifugalKing]

Ah, looking at the diagram again, I think 3 might actually be correct. If you look at the first circle around 2 it seems to be around half the radius of 1 so I'd assume that the circles about 2 are 0.5λ, 1.5λ, 2.5λ... So you should probably take another look at R2 for Q.

So R2 for Q would be 1 as opposed to 2?

 

[MikeN]

The first circle appears to be 0.5λ away from 2, each other one appears to be spaced 1λ apart.

 

[CentrifugalKing]

The first circle appears to be 0.5λ away from 2, each other one appears to be spaced 1λ apart.

So 1.5?

 

[MikeN]

I think that'd be correct. As for the C/D column, if these circles are one wavelength apart then the circles must represent unique points on the wave over one wavelength. If you consider a sine/cosine curve over one wavelength you can see that all values of y appear for 2 values of x with the exception of the peak and the trough, therefore the circles must represent either a peak or a trough. If you imagine the peaks to be at the circles then the troughs should be mid way between the circles.

 

[CentrifugalKing]

Okay I've updated. Mind telling me if this is sound?

R1 R2. Chng. R c/d
P. 2. 3. 1. C
Q. 3. 1.5. 1.5. D
R. 2.5. 3. 0.5. D

 

[MikeN]

Sorry, didn't see that you'd responded. You've probably submitted your solution by now, but just incase you're still on it, I think that everything is correct except for the C/D column. If the circles represent peaks then, for example, with P it's on a peak for 1 and a trough for 2 causing destructive interference.