Two Point Source Interference pattern

[John H]

Homework Statement

Studying physics in High school, and for two years now we have covered two point source interference patterns with light, sound, and water wave in a ripple tank per say. The type of wave nor medium is necessary significant for me at the moment, but I am having trouble understanding something about the interference pattern, the shape and spreading of nodal, and anti nodal lines.

http://www.physicsclassroom.com/class/light/u12l3b.cfm

like ones depicted in above site. I Have at moment at my availability 3 different textbooks which all state that indeed there is a fixed number of nodal lines, and I always though there would be an infinite number of nodal lines, I know this isn't that important, but I just don't see why there wouldn't be many nodal line (Lines of destructive interference present), I know waves diminish, they spread losing energy and thus amplitude, but say they didn't which is what my books assume, why wouldn't there be infinite many nodal lines.

Also, sources are in phase, and nothing is changing over time.

Homework Equations

No real relevant equations I know of, just the concepts.

The Attempt at a Solution

I though it had something to do with loss of energy as stated above, but books are talking about ideal waves, which don't seem to lose energy.

 

[graphene]

yes, if you take your space to be infinitely large, there will be infinite number of nodes antinodes (& everything in between).

 

[Redbelly98]

Homework Statement

Studying physics in High school, and for two years now we have covered two point source interference patterns with light, sound, and water wave in a ripple tank per say. The type of wave nor medium is necessary significant for me at the moment, but I am having trouble understanding something about the interference pattern, the shape and spreading of nodal, and anti nodal lines.

http://www.physicsclassroom.com/class/light/u12l3b.cfm

like ones depicted in above site. I Have at moment at my availability 3 different textbooks which all state that indeed there is a fixed number of nodal lines, and I always though there would be an infinite number of nodal lines, I know this isn't that important, but I just don't see why there wouldn't be many nodal line (Lines of destructive interference present), I know waves diminish, they spread losing energy and thus amplitude, but say they didn't which is what my books assume, why wouldn't there be infinite many nodal lines.

To start, just consider the straight line segment joining the 2 sources. You could work out how many nodal lines pass through that segment, using the fact that the path difference to the sources is (n+½) times the wavelength. That's just a finite number of points on that segment, through which the nodal lines intersect.

Next consider the rest of the straight line joining the 2 sources -- not the segment in between, but the parts of the line on either side of the source points. How many points on that line have a path difference of (n+½) times the wavelength?

The end result is a finite number of nodal lines.

 

[John H]

To start, just consider the straight line segment joining the 2 sources. You could work out how many nodal lines pass through that segment, using the fact that the path difference to the sources is (n+½) times the wavelength. That's just a finite number of points on that segment, through which the nodal lines intersect.

Next consider the rest of the straight line joining the 2 sources -- not the segment in between, but the parts of the line on either side of the source points. How many points on that line have a path difference of (n+½) times the wavelength?

The end result is a finite number of nodal lines.

Thanks, now that I think about its pretty obvious that there is finite nodal lines.

 

[graphene]

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