# Analyzing Wave Interference Patterns

1. Sep 27, 2013

### Hapablap

I don't know if this would be considered a homework problem, so I hope I'm posting in the right place. I'm working through an independent learning course and just needs some help with the terminology in the book. It started expressing wavelengths in 1/2λ, and I can't find an explanation why. I've come to this point in the text:

http://img542.imageshack.us/img542/1317/ovlt.jpg [Broken]

It states: "Since each circle in Figure 13.25 corresponds to a wave, the distance between each circle is one wavelength, or 1 1/2λ. Therefore, the distance from the Source S1 to the point P1 on the first nodal line is 3λ. Similarly, the distance between S2 and P1 is 2.5 1/2λ. Therefore, the difference in the distance between the line segments P1S1 and P1S2 is 0.5 1/2λ."

I assumed each circle is a crest in the wave, so a full wavelength. Are they actually crests and troughs alternating to make them half wavelengths? But then why is the distance from S1 to P1 3λ and not expressed as 1/2λ? Also, the part where it states "the distance between each circle is one wavelength, or 1 1/2λ" seems to be contradictory. Is it one wavelength or one half wavelength?

Any help understanding this would be greatly appreciated!

Last edited by a moderator: May 6, 2017
2. Sep 27, 2013

### Delphi51

You are clearly more knowledgeable than the person who wrote the caption!!
Indeed those are contradictory.
And "the distance from the Source S1 to the point P1 on the first nodal line is 3λ" doesn't make sense either way. The distance from S2 to P1 has to be 2.5 wavelengths so that a crest from S1 meets a trough from S2.

I always taught my grade 11 students to draw the crest circles with solid lines and the trough circles with dashed lines (or make them different colors). Like this one for "interference through a double slit" in the 2nd diagram: http://www.rpi.edu/dept/phys/ScIT/InformationStorage/intdiff/intdiff.html

Note that the heavy n=1 lines in your question's diagram go through points where there is a circle from one source and halfway between circles from the other source. This tells me that only the circles for crests are shown. Trough circles are to be imagined half way between every two crest circles. The heavy n=1 lines are where a crest from one source meets a trough from the other source; they are nodal lines or lines of destructive interference.

3. Sep 28, 2013

### Hapablap

That helps, thank you for the response :)

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