What Determines the Distance Between Two People Based on Interference Patterns?

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SUMMARY

The discussion focuses on determining the distance between two people using interference patterns in sound waves. Key concepts include wave velocity, defined as the product of frequency and wavelength, and the application of single-slit diffraction principles. The participants emphasize the significance of the doorway's width in wavelengths and trigonometric methods for calculating distances. The mathematical approach to solving this problem involves understanding how sound waves interact when passing through narrow openings.

PREREQUISITES
  • Understanding of wave velocity, specifically the equation: wave velocity = frequency * wavelength
  • Familiarity with trigonometric functions for distance calculations
  • Knowledge of single-slit diffraction and its implications on wave behavior
  • Basic principles of sound wave interference
NEXT STEPS
  • Study single-slit diffraction patterns and their mathematical derivations
  • Learn about sound wave interference and its applications in real-world scenarios
  • Explore trigonometric methods for calculating distances in physics problems
  • Investigate the effects of doorway dimensions on sound wave propagation
USEFUL FOR

Students in physics, particularly those studying wave mechanics, sound engineers, and anyone interested in the mathematical modeling of sound wave interactions.

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Homework Statement



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Homework Equations



wave velocity = frequency * wave length

The Attempt at a Solution



Well...I'm not sure. I know how you could find the distance to the person to the right using trigonometric, but I don't know how to actually answer the question (mathematically). Interference might have something to do with it?
 
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The width of the doorway (in wavelengths) should be important.

Consider having one whistle, and two echos (one from each side).

Regards,

Bill
 
bfr said:

The Attempt at a Solution



Well...I'm not sure. I know how you could find the distance to the person to the right using trigonometric, but I don't know how to actually answer the question (mathematically). Interference might have something to do with it?

Yes; the sound wave is passing through a wide slit, so this is a single-slit diffracion problem.
 

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