### Doppler graph

Source velocity (in units of the speed of sound)
-1 +1
0.0
Source position (m)
-50 +50
-20
Observer velocity (in units of the speed of sound)
-1 +1
0.0
Observer position (m)
-50 +50
20

This is a simulation of the Doppler effect. You can set both the initial position and the velocity of the source (the small blue dot). and the initial position and the velocity of the observer (green rectangle), and then see the pattern of waves emitted by the source as the waves wash over the observer. The source emits a frequency of 100 Hz when the source is at rest. fo represents the observed frequency (the one heard by the observer).

The simulation also shows a graph of the frequency shift, expressed as a fraction of the emitted frequency (100 Hz). For instance, if you start with the observer at rest, to the right of the source, and then set the source velocity to be 0.2 times the speed of sound, the observed frequency is 125 Hz. That is 0.25 times 100 Hz above 100 Hz, so the graph shows a red dot at +0.25 on the y-axis (and +0.2 on the x-axis). When the source passes the observer, the observed frequency drops to 83 Hz, a drop of 17 Hz (0.17 times 100 Hz), so the red dot shifts to -0.17 on the y-axis, and -0.2 on the x-axis, to reflect the fact that the observer's relative motion is now away from the source.

What about the lines on the graph? The green line just shows the effect of the observer motion only - it is plotted as a function of observer velocity. This shows a linear relationship with observer velocity. If you set the observer velocity to zero, you also get one blue curve - this is the frequency shift plotted as a function of source velocity. (Yes, the two graphs are plotted as a function of different velocities!) The fact that the green line and the blue curve are not the same tells us that the Doppler effect for sound waves is not just a relative velocity effect - the source moving at some velocity relative to the air toward a stationary observer is not the same as the observer moving at that velocity toward a stationary source. At low speeds, these are approximately the same, but as the relative speed increases the difference becomes more apparent.

If you set the observer velocity to some non-zero value, the blue curve separates into two curves, one that applies when the source is to the left of the observer and the other for when the source is to the right of the observer. (These blue curves account for both the observer motion and the source motion). The dot with the red center shows the current frequency shift. In a situation in which the source moves to the other side of the observer, the red point will move to the other curve, as the observed frequency changes.

Simulation first posted on 3-3-2017. Written by Andrew Duffy

This work by Andrew Duffy is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
This simulation can be found in the collection at http://physics.bu.edu/~duffy/classroom.html.

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