Finding path difference of EM waves received by radio telecopes

Click For Summary
SUMMARY

The discussion centers on the calculation of path difference for electromagnetic (EM) waves received by radio telescopes. The initial confusion arose from the incorrect use of trigonometric functions, where the user mistakenly identified the path difference as ##x = d \sin \theta## instead of the correct formula ##x = d \cos \theta##. The user later acknowledged the error and emphasized the importance of verifying results against extreme cases, such as ##\theta = 0## and ##\theta = \pi/2##. This highlights the critical nature of understanding trigonometric relationships in wave physics.

PREREQUISITES
  • Understanding of trigonometric functions, specifically sine and cosine.
  • Familiarity with electromagnetic wave theory.
  • Basic knowledge of radio telescope operation and signal processing.
  • Ability to analyze geometric relationships in physics problems.
NEXT STEPS
  • Study the derivation of path difference formulas in wave mechanics.
  • Learn about the applications of trigonometry in physics, particularly in wave interference.
  • Explore the principles of radio telescope design and signal analysis.
  • Review extreme case analysis in mathematical physics to enhance problem-solving skills.
USEFUL FOR

Students of physics, radio astronomers, and anyone involved in the study of electromagnetic wave propagation and interference patterns.

songoku
Messages
2,508
Reaction score
402
Homework Statement
Please see below
Relevant Equations
Trigonometry
1626158609238.png


My attempt:
1626158751799.png

I think ##x## is the path difference so by using trigonometry, I got ##x=d \sin \theta##

But my teacher said the answer is ##d \cos \theta##

What is my mistake? Thanks

Edit: Sorry, I found my mistake. My ##x## is not the path difference
 
  • Like
Likes   Reactions: rsk
Physics news on Phys.org
OK, well done.

Tip: Always check a result for extreme cases (like here: ##\theta = 0## and ##\theta = \pi/2##)

##\ ##
 
  • Like
Likes   Reactions: songoku
songoku said:
My x is not the path difference
Well, it is the difference between the path lines, but not the path length difference.
 
  • Like
Likes   Reactions: songoku
Thank you very much BvU and haruspex
 
  • Like
Likes   Reactions: berkeman and BvU

Similar threads

  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K
Replies
14
Views
2K
  • · Replies 6 ·
Replies
6
Views
998
Replies
20
Views
5K
  • · Replies 10 ·
Replies
10
Views
2K
Replies
27
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K