2D Doppler Shift / Relative Velocities

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SUMMARY

This discussion focuses on adapting the Doppler shift formula for a stationary listener when the source moves in a two-dimensional path, specifically when a train moves from west to east while the listener faces north. The key formula for the frequency factor in the one-dimensional case is v / (v - 333 m/s). The challenge arises in calculating the relative velocity of the source concerning the listener, as the absolute velocity cannot be directly applied. The conversation highlights the need for a proper understanding of relative motion in two dimensions to accurately compute Doppler effects.

PREREQUISITES
  • Understanding of the Doppler effect and its mathematical representation
  • Familiarity with relative velocity concepts in physics
  • Knowledge of two-dimensional motion analysis
  • Basic principles of wave frequency and sound propagation
NEXT STEPS
  • Research the mathematical derivation of the Doppler shift in two dimensions
  • Study relative velocity calculations in non-linear motion scenarios
  • Explore applications of Doppler shift in air intercept missile guidance systems
  • Review the textbook referenced for detailed explanations on line of sight rate changes
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Physicists, engineering students, and professionals involved in acoustics or motion analysis, particularly those interested in the applications of the Doppler effect in real-world scenarios.

awelex
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Hi,

I'm trying to adapt the doppler shift formula for a stationary listener and a source traveling in a straight line towards/away from the listener to the case where the source does not move straight towards the listener. For example, suppose that I am looking north and train further in the distance moves from west to east.

The frequency factor in the 1D case is \frac{v}{v - 333m/s}. The only thing that changes in the 2D case is that we can't no longer use the absolute velocity v of the source, but have to use the relative velocity with respect to the listener. But this is where I'm stuck: How do I compute this relative velocity when the listener is stationary? Wouldn't that mean that v_{rel} = v_{abs} - 0 = v_{abs}? That obviously can't be true.

Thanks,
Alex
 
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