Interference of two radio waves

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SUMMARY

The discussion focuses on calculating the distance from source A for constructive interference between two coherent radio wave sources, A and B, which are 5.00 meters apart with a wavelength of 6.00 meters. The equation used is r1 - r2 = mλ, where r1 is the distance from A to the point of interference (P) and r2 is the distance from P to B. The correct distance for the first instance of constructive interference is determined to be 2.5 meters from source A, achieved by applying the equation with m=1. The discussion highlights the importance of understanding the integer values of m for multiple points of constructive interference.

PREREQUISITES
  • Understanding of wave interference principles
  • Familiarity with the concept of coherent sources
  • Knowledge of wavelength and its role in interference
  • Ability to apply basic algebraic equations
NEXT STEPS
  • Study the principles of wave interference in detail
  • Explore the effects of varying the distance between coherent sources
  • Learn about the application of the equation r1 - r2 = mλ for different values of m
  • Investigate the concept of destructive interference and its calculations
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics, as well as educators seeking to explain the principles of wave interference and coherent sources.

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Homework Statement



Two coherent sources of radio waves, A and B, are 5.00 meters apart. Each source emits waves with wavelength 6.00 meters. Consider points along the line connecting the two sources.

At what distance from source A is there constructive interference between points A and B?

Homework Equations



Let P be the point of constructive interference:

r_1 - r_2 = m\lambda where r_1 is the distance from A to P and r_2 is the distance from P to B.

These were the hints given, and don't make sense.

The Attempt at a Solution



I got the answer of 2.5 metres by drawing a diagram and estimating where the two waves would cross (constructive interference). The answer was correct, a lucky guess...

I don't know how to apply that equation. Does it need to be applied twice? For m I would use the value of 1?
 
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m could be any integer, not just 1.

Try m = 0 or 1, and see what you can come up using your equation,

r1 - r2 = m λ​
 

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