The discussion focuses on calculating the number of antinodal and nodal lines for two coherent sources vibrating in phase, separated by a distance of 4.5 wavelengths (λ). The established formulas indicate that the number of antinodal lines is calculated as 2 times the floor function of the separation over wavelength plus one, resulting in 9 antinodal lines. The number of nodal lines is determined as twice the floor function of the separation over wavelength, yielding 8 nodal lines. The conversation also addresses the implications of endpoint counting and variations in separation, confirming the correctness of the initial calculations under specified conditions.
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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?