The v value in (c+v)(c-v) mathematics is a dynamic variable that may change any moment. Speeds of reference systems, their directions and their locations at a specific time are the components that determine the value.

In the animations here, you can see how v value occurs in Doppler Triangles and Doppler Quadrangles in detail in the animations here. No mathematical equations are used here. You can access the information about the mathematical equations in the pages “Doppler Triangle” and “Doppler Quadrangle”.

You can use the animation for both the Doppler Triangle and the Doppler Quadrangle.
You can drag the red points in the animation anywhere you like and do analyses for different situations. 
In the animation, the reference systems are sending signals towards each other.
The slider bar simulates the travel time between the moment the signal broadcast and arrival.

  • Blue arrow(s) shows the distance that the plane(s) covers within the travel time.
  • When the slider bar is in its final position (arrival time of the signal), the animation shows the locations of the Image Objects.
  • The Black Arrows that are seen when the slider bar is in its last position show how v value occurs for each reference system in the existing situation. 
    As can be seen in the animation, the Black Arrows are always equal to each other in size and this shows that v value is a common value for both reference systems.
  • The text boxes on the right bottom show the speeds of the reference systems for the situation that is set and they give the v value by calculating it.

The black arrows that represent the v value show distances, not speeds, in the animation. x=v.tΔ
Let me give you a reminder about the v value here.
±v value shows, on its own, the speed of moving-away/approaching speed of two reference systems relative to each other. Additionally, it is a value that shows the amount of deviation from the speed of light. When it is written as a component of c, i.e. (c±v), it is now the signal speed. It indicates the speed of the signal that it sends relative to the reference system that sends the signal.

The Radio Buttons set the run mode as the Doppler Triangle or the Doppler Quadrangle. 
Check Boxes control the visibility of the existing lines. 

The animation here is the animated version of the animation above. After setting the animation to any position and clicking on the Play button, the plane(s) will move in the direction of the blue arrow. 

I suggest you play the animation when you move the Slider Bar to its final position.

The aim of this simulation is to shed some light on the variability of the v value. When the plane(s) are in motion, you can follow the changes on the v value in the text box showing the value on the bottom right corner.
Demo Buttons: They set the animation for a situation that can be watched comfortably. The animation will start as soon as you click on the Play button.
Reset Button: The animation goes back to the situation in the moment when the Play button was clicked on.
Free Button: It lets you set the animation.

There is another point that I’d like you to pay attention. As can be seen in the animation, the speeds of the Source Object and the Image Object are not equal. This difference is called “Speed Shift”. You can access the topic Speed Shift in the part Publications After the Book.

Go back to the Animation List Page