# Circular Wave Fronts Emitted by Two Wave Sources

• CentrifugalKing
If the circles represent troughs then, for example, with P it's on a trough for 1 and a peak for 2 causing constructive interference.f

## 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?

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

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

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?

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

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

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.

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

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.

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?

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

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

So 1.5?

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.

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

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.