The discussion revolves around determining the number of antinodal and nodal lines produced by two coherent sources vibrating in phase, separated by a distance of 4.5 wavelengths. Participants are exploring the implications of the separation distance on the resulting interference pattern.
The discussion is active, with participants questioning the assumptions regarding the counting of lines and the implications of the separation distance. Some guidance has been offered regarding the interpretation of the formula, but no consensus has been reached on the specifics of counting lines or the impact of slight variations in separation.
Participants note the ambiguity in the problem statement regarding the counting of lines at the endpoints and the potential for infinite lines if not constrained to a specific region. The discussion also touches on the nuances of the formula used for calculating nodal lines.
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.superconduct said:Homework Statement
For two coherent sources vibrating in phase separated by 4.5(lambda), what are the numbers of antinodal and nodal lines?
Homework Equations
No. of nodal lines equals twice the floor function of separation over wavelength.
The Attempt at a Solution
No. of antinodal lines= 2(4)+1=9
No. of nodal lines= 2(4)=8
Is this correct?
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?haruspex said: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.
No, sorry, forget the bit about infinity.superconduct said: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?
Do you mean the two lines on the plane joining the sources and with a path difference of 4.5 lambda ?haruspex said: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.
yessuperconduct said:Do you mean the two lines on the plane joining the sources and with a path difference of 4.5 lambda ?
If the separation becomes 4.4999999lamba instead of 4.5, then is my answer above correct?haruspex said:yes
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.superconduct said:If the separation becomes 4.4999999lamba instead of 4.5, then is my answer above correct?