When a wave emitting source is moving, the observed frequency changes. This is known as the Doppler effect. Here you will see animations of the Doppler effect for a source moving with a constant velocity and in circular motion. The circular motion is interesting and you may have seen a demonstration of the resulting Doppler effect from a twirling buzzer. When the speed of the motion vs is faster than the wave speed c, a V-shaped row wave is produced if the source is moving with a constant velocity. The shock structure is more complicated in circular motion. The mathematical detail and animation setup is explained in this documentation.
A point source (represented by a black dot) is moving with a constant velocity toward the right with a speed vs. The source is emitting waves at a frequency f. Each red circle represents the wave crest emitted by the source. Click the "Play Animation" button below to see the animation. The parameters vs and f can be changed using the following table.
Size of the box = 10 s-1/c
Click the "Pause" button to pause and "Resume" to resume the animation. If you change the parameters in the table, click the "Replay" button to start a new animation.
Since the wave is traveling with the same speed in all directions as seen by a stationary observer, the observed frequency is inversely proportional to the observed wavelength. As seen from the animation, the observed wavelength (the distance between adjacent red lines) is shorter (i.e. higher frequency) when the source is moving towards the observer and longer (i.e. lower frequency) when it is moving away from the observer. You can also measure the frequency of the wave at a given point by counting the number of red lines passing through it at a fixed time interval.
Be sure to try vs > c (e.g. vs = 2c) to see the development a bow wave.
Here a point source (represented by a black dot) is moving with a constant speed in a circle of radius rs. At a fixed position, the observed frequency changes periodically as the source goes in circle, except at the center of the circular motion marked by "o". You can measure the observed frequency at "o" by counting the number of red lines passing through it at a fixed time interval.
"o" is the center of the circular motion. Blue lines represent the locations of shock waves (appear only when vs ≥ c).
Click the "Pause" button to pause and "Resume" to resume the animation. If you change the parameters in the table, click the "Replay" button to start a new animation.
Try vs = 2c, f = 10 Hz, L = 15 s-1/c and rs = 1 s-1/c. Can you explain the observed pattern? Does a shock wave ever hit the center "o"?