Nodal Lines from Two Point Sources: Solving for d/lambda

[Barry Melby]

How many nodal lines are created by two point sources emitting at the same wavelength that are separated by a distance equal to 4.5*lambda?

I used the equation 2(d/lambda) which in this case equals 9, but I've been told this is incorrect. Where have I gone wrong?

 

[mfb]

Did you draw a sketch?

 

[Barry Melby]

yes, i drew a sketch and 9 nodal lines seems correct.

 

[mfb]

Hmm... 9 looks correct if the two point sources emit in phase.

 

[Mgl003]

There are 10 nodal lines, because the one in the middle is an anti-nodal line. So there are 7 anti - nodal lines. Because the wavelength difference is 4.5, doesn't make sense to have one less nodal line.

 

[haruspex]

There are 10 nodal lines, because the one in the middle is an anti-nodal line.

It is an even number, yes, but the question is unreasonable in that the given distance is itself an odd number of half wavelengths. There is no way it would be exactly so in practice, and the answer changes according to whether it is just slightly more or slightly less.