What is the Path Difference: Waves

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SUMMARY

The discussion focuses on calculating the path difference between sound waves emitted from two in-phase speakers that are 4.50 m apart, emitting 1690 Hz sound waves in a room where the speed of sound is 343 m/s. The correct approach involves determining the hypotenuse of the triangle formed by the speakers and the observation point, which is 9.6178 m. The path difference must then be converted from meters to wavelengths by dividing the path difference in meters by the wavelength, calculated as 0.203 m. The final path difference in wavelengths is approximately 47.5 wavelengths.

PREREQUISITES
  • Understanding of wave properties, specifically sound waves.
  • Knowledge of basic trigonometry to calculate distances in a triangle.
  • Familiarity with the concept of wavelength and its relationship to frequency and speed of sound.
  • Ability to perform unit conversions, particularly from meters to wavelengths.
NEXT STEPS
  • Calculate the wavelength of sound waves using the formula: wavelength = speed of sound / frequency.
  • Explore the concept of constructive and destructive interference in wave physics.
  • Learn about the application of the Pythagorean theorem in wave problems.
  • Investigate the effects of path difference on sound intensity and phase at different points in a room.
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics, acoustics, and sound wave interference patterns.

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Homework Statement


Two in-phase speakers 4.50 m apart in a plane are emitting 1690 Hz sound waves into a room where the speed of sound is 343 m/s. Consider a point that is 8.50 m in front of one of the speakers, perpendicular to the plane of the speakers. What is the path difference (in wavelengths) between the two sound waves at this point?


Homework Equations


Hypotenuse Equation...


The Attempt at a Solution


Since the speakers are 4.50 m apart, and the point is perpendicular to one of the speakers, it essentially makes the shape of a triangle. I find the hypotenuse, which is 9.6178 m, and then subtract 8.50 m from it to find the path difference. But that answer is not right :( What should I be doing..?
 
Physics news on Phys.org
You've got the path difference in meters, but the question asks for the path difference in wavelengths. You're halfway there.
 

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