Understanding Phase Difference in 3D Waves

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SUMMARY

The discussion focuses on calculating the phase difference between two points in a 3D wave scenario, given a wave speed of 346 m/s and a frequency of 13100 Hz. The correct formula for phase difference in three dimensions involves using the distance from the origin to each point rather than a one-dimensional approach. The user initially attempted to apply the one-dimensional phase difference formula, which led to confusion. The solution requires calculating the distances of each point from the origin and then applying the phase difference formula accordingly.

PREREQUISITES
  • Understanding of wave mechanics and properties, including wave speed and frequency.
  • Familiarity with the concept of phase difference in wave physics.
  • Knowledge of 3D distance calculations and geometry.
  • Ability to apply mathematical formulas to physical scenarios.
NEXT STEPS
  • Study the derivation of the phase difference formula for three-dimensional waves.
  • Learn about spherical wave propagation and its implications on phase calculations.
  • Explore the relationship between wave speed, frequency, and wavelength in various media.
  • Investigate practical applications of phase difference in fields such as acoustics and optics.
USEFUL FOR

Students and professionals in physics, particularly those studying wave mechanics, as well as engineers working with wave propagation in three-dimensional spaces.

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Homework Statement



A wave at the origin expands outwards passing the points (.01, .03, .02) and (-.01, .015, .025). This wave has a wave speed, V_w = 346 m/s and frequency = 13100 HZ.

What is the phase difference between these two points?


Homework Equations




v = (wavelength)(frequency)

Phase Difference = 2pi (delta x) / Wave length


The Attempt at a Solution



I attempted to use the following:


[(distance between points using 3D formula)/(wave length)] * 2pi = phase difference.


This was in correct. I am going to guess that it's because "Phase Difference = 2pi (delta x) / Wave length" is for a wave in one dimension. My question is how does the phase difference change in 3 dimensions? I attempted to use the surface area of a sphere but it also failed. Something is quite wrong.
 
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Use the distance from the origin... the delta you need is the difference of the second point from the origin - the distance of the first point from the origin.
 
Wonderful thanks.
 

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