Waves - A two-source interference problem

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SUMMARY

The discussion focuses on calculating the angle to the first point of minimum signal (m=0) for two synchronized radio towers transmitting at an AM frequency of 1000 kilohertz, with a wavelength of 300 meters. The separation between the towers is 400 meters, and the road is located 5 kilometers away. The correct approach involves using the formula for destructive interference, specifically dsin(theta) = m x lambda, to find the angle in radians.

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  • Understanding of wave interference principles, particularly destructive interference.
  • Familiarity with the formula dsin(theta) = m x lambda.
  • Knowledge of radio wave properties, including frequency and wavelength calculations.
  • Basic concepts from Young's double-slit experiment.
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  • Study the principles of wave interference in more depth.
  • Learn how to derive and apply the formula for destructive interference in various contexts.
  • Explore the relationship between frequency, wavelength, and wave speed in electromagnetic waves.
  • Investigate practical applications of interference patterns in telecommunications.
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fatkat444
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Consider a road that runs parallel to the line connecting a pair of radio towers that transmit the same station (assume that their transmissions are synchronized), which has an AM frequency of 1000 kilohertz. If the road is 5 kilometers from the towers and the towers are separated by 400 meters, find the angle to the first point of minimum signal (m=0). Hint: A frequency of 1000 kilohertz corresponds to a wavelength of 300 meters for radio waves.
Express your answer in radians, to two significant figures.




Because it's constructive interference i think we use dsin(theta) = m x lambda



So that would be: 400 x sin(theta) = 0 x 300

Is this correct? And if so how would you go about working it out?
 
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I am guessing you have studied Youngs double slit experiment. This is very similar to that, but you have to use formula for destructive interference, since they have asked for the minima.

Consider the two towers as sources and the road as the screen in youngs DS Expt...
 
Raze2dust said:
I am guessing you have studied Youngs double slit experiment. This is very similar to that, but you have to use formula for destructive interference, since they have asked for the minima.

Consider the two towers as sources and the road as the screen in youngs DS Expt...

OK, Thanks a lot.
 

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