# Path difference between the waves

Tags:
1. Nov 2, 2015

### toforfiltum

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
I formed a right angle triangle between the arrow downwards,d, and perpendicular line x from arrow. As such, sin θ = x/d.

x= d sinθ
path difference: d sinθ/λ

My answer is C, but answer is B. Where did cos θ come from?

2. Nov 2, 2015

### Staff: Mentor

Looking at the figure, in which case would you expect it to be no difference in path length?

3. Nov 2, 2015

### Staff: Mentor

Your description of how you formed your triangle is not very rigorous, so I may be misinterpreting what you've described. That said, I think you've allocated angle $\theta$ to the wrong corner of your triangle.

Perhaps you could sketch your construction on the image and post the result?

4. Nov 2, 2015

### toforfiltum

Is it when the waves are received at angle perpendicular to the horizontal?

5. Nov 2, 2015

### Staff: Mentor

Which corresponds to which value of θ?

6. Nov 2, 2015

90°?

7. Nov 2, 2015

### toforfiltum

I did it this way, but I think now I'm wrong to assume that x is parallel to the wavelength, right?

8. Nov 2, 2015

### Staff: Mentor

You've drawn the correct triangle but as you say, you've chosen the wrong "leg" for x. You want the leg that lies along the wave's path.

9. Nov 2, 2015

### toforfiltum

Ah, I see now why it's cos θ. But, why it is not D now? Shouldn't path difference be expressed in terms of fraction of wavelengths?

10. Nov 2, 2015

### Staff: Mentor

In this case the path difference is just the length, otherwise the problem would have specified to express it in terms of wavelengths.

11. Nov 2, 2015

Ok. Thanks!