How many nodal lines for two point sources at 2.5 lamda separation?

In summary, the conversation discusses determining the number of nodal lines created by two point sources emitting at the same wavelength and separated by a distance equal to 2.5 lamda. A formula from the textbook is used to calculate the number of nodal lines, with an initial answer of 5. However, after considering the placement of nodal lines and referencing the textbook, it is determined that the correct answer is actually 10.
  • #1
MaryCate22
22
0

Homework Statement


How many nodal lines are created by two point sources emitting at the same wavelength that are separated by a distance equal to 2.5 lamda?

Homework Equations


My textbook says, "If two coherent sources located a distance d apart emit identical waves of wavelength lamda, then the number of nodal lines on either side of a straight line running through the centers of the sources is the greatest integer smaller than or equal to 2(d/lamda)."

The Attempt at a Solution


Using the formula from the textbook I get 5 nodal lines. But this answer is incorrect. I've also tried 3 based on the fact that nodal lines occur in places where the path difference from the sources are some 0.5 lamda, 1.5 lamda, 2.5 lamda,... etc. I'm thinking based on the quote from the textbook that I need to double my answer of five since the answer is just for one side of a line running through the center of the sources. I really don't want to lose anymore credit however. Any hints?
 
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  • #2
Never mind you guys, I solved it. N=10 was in fact the correct answer. Sorry y'all.
 

1. How do you determine the number of nodal lines in a given system?

The number of nodal lines in a system can be determined by solving the Schrödinger equation for the system. The number of solutions to the equation represents the number of nodal lines.

2. Can the number of nodal lines change in a system?

Yes, the number of nodal lines in a system can change depending on the energy of the system. As the energy increases, the number of nodal lines can change.

3. What is the significance of nodal lines in quantum mechanics?

Nodal lines represent the points in a system where the wave function is equal to zero. They play a crucial role in understanding the behavior and properties of quantum systems.

4. Are nodal lines only present in quantum systems?

Nodal lines can also be found in classical wave systems, such as vibrating strings or drums. However, they have a different physical interpretation in these systems compared to quantum systems.

5. Can nodal lines be observed experimentally?

Yes, nodal lines can be observed experimentally using various techniques such as scanning tunneling microscopy or photoemission spectroscopy. These techniques allow for the visualization of the wave function and the nodal lines in a system.

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