Doppler Shift in 2D

[kjiang]

Quick question.

From

https://en.wikipedia.org/wiki/Doppler_radar

“This variation of frequency also depends on the direction the wave source is moving with respect to the observer; it is maximum when the source is moving directly toward or away from the observer and diminishes with increasing angle between the direction of motion and the direction of the waves, until when the source is moving at right angles to the observer, there is no shift.” (Talking about Doppler Shift)

So if we have a setup in the attachment below...

By using the doppler equation, the velocity of the object can be determined. Is it the velocity of the object labeled 'v' or is it the velocity directed towards the source (which emits the signal)? If it was the latter, then how does that make sense? How can there be a velocity directed towards the source if there is no movement in that direction? Thanks!

 

[EdStainless]

The V determined by Doppler shift is the component of the velocity that is either directly toward or away from the observer.
In practice most of these types of radar are measuring both the time delay and the doppler shift. By combining the two pieces of information you can arrive at the actual velocity (speed and direction) of the target.
As a common 2-d example picture standing along the fence along the back straight at a race track, as a car approaches it is nearly headed straight toward you and you hear the upward shift in frequency, when it is directly in front of you there is no relative V so you hear the base frequency, and as it moves away again the speed of the car and the V in line away from you are nearly identical and you hear the shift downward. It is straight forward to use this to measure the actual speed of a car on a race track, you never need to measure the actual frequency, just compare them.

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P.E. Metallurgy, Plymouth Tube

 

[IRstuff]

This is high school vector math; at any position other than direct opposition, the spherical waves from the source interact with the velocity vector, which can be decomposed into a radial and tangential component, relative to the spherical wavefront. The tangential component induces no Doppler effect, only the radial component.

TTFN
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