# Homework Help: Determining the number of antinodal and nodal lines

1. Jan 19, 2016

### superconduct

1. The problem statement, all variables and given/known data
For two coherent sources vibrating in phase separated by 4.5(lambda), what are the numbers of antinodal and nodal lines?

2. Relevant equations
No. of nodal lines equals twice the floor function of separation over wavelength.

3. The attempt at a solution
No. of antinodal lines= 2(4)+1=9
No. of nodal lines= 2(4)=8

Is this correct?

2. Jan 19, 2016

### haruspex

Are you supposed to count nodes at the endpoints? The question as you've posted it does not even limit it to the space between the sources, so you could argue there's an infinity of each.

3. Jan 19, 2016

### superconduct

What does it mean by endpoints here? How are there an infinity of nodal and antinodal lines? Under what conditions will the number be limited?

4. Jan 19, 2016

### haruspex

No, sorry, forget the bit about infinity.
But for the endpoints, I mean nodal lines straight out to the side from the two sources. In this set-up, if you move from one source directly away from the other source, they will cancel all the way along that line, no? Same for the other source. Are these two lines counted? The formula you quote implies not.

5. Jan 20, 2016

### superconduct

Do you mean the two lines on the plane joining the sources and with a path difference of 4.5 lambda ?

6. Jan 20, 2016

### haruspex

yes

7. Jan 20, 2016

### superconduct

If the separation becomes 4.4999999lamba instead of 4.5, then is my answer above correct?

8. Jan 20, 2016

### haruspex

Yes I think so, it's just the special case of n+1/2 I was asking about. It seems to me the formula you quote doesn't quite work there.