Applet by Wolfgang Christian
General Discussion: The animation above demonstrates the doppler shift of a wave that results from the motion of the source producing the wave. The expanding circles in the animation may be thought of as wave fronts. Notice that the distance between these circles depends on direction. For example, the distance between the wave fronts in front of the source are more closely spaced together than the wave fronts behind the source. We therefore conclude that the wavelength also depends on direction because the distance between successive wave fronts corresponds to the wavelength of the wave. In particular, the wavelength emitted ahead of the source will be shorter than it would have been had the source been at rest. Conversely, the wavelength emitted behind the source will be longer than it would have been had the source been at rest. More generally, the degree by which the wavelength is shortened or lengthened depends on the angle between the direction in which the source is moving and the line of sight connecting the source to the observer.
The degree by which the wavelength is shortened or lengthened, along a given direction, also depends on the speed of the source. To be more precise, it depends on the speed of the source relative to the medium in which the wave is propagating in the case of a classical wave (e.g., sound, waves on the surface of water, and pretty much any type of wave other than electromagnetic waves) and the speed of the source relative to the observer in the case of a relativistic wave (i.e., electromagnetic waves which include, but are not limited to, xrays, light, infrared light, etc.). Choose which of these two cases you wish to study by checking either the box marked "Classical" or the box marked "Relativistic". You may then set the speed of the source by either sliding the bar marked "speed" or by typing in a speed, and then pressing enter on your keyboard, in the form field to the right of this bar. Either way, the speed is shown in this same form field and is given in units of the speed of wave that is appropriate to that medium in the case of classical waves or in units of the speed of light in the case of relativistic waves. Thus, the maximum value that you can set the speed in the case of relativistic waves is 0.99 (times the speed of light in a vacuum) whereas maximum value that you can set the speed in the case of classical waves is 1.92 (the maximum value in the case of classical waves is a constraint imposed by the program and does not correspond to any constraints imposed by the physics of the situation). The source is traveling faster than the speed of waves in that medium when the speed is set to a value greater than 1 in the case of classical waves. Sonic booms are an application of the situation mentioned in the preceding sentence.
On important consideration to keep in mind when working with classical waves is that this animation only takes into account the motion of the source relative to the medium that the wave is propagating in. The animation does not take into account the doppler shift resulting from the motion of the observer relative to the medium that the wave is propagating in. Both effects must be taken into account for a complete description of the doppler shift for the case of classical waves. Such considerations do not enter in the case of relativistic waves because the only relevant speed in the case of relativistic waves is the speed of the source relative to the observer.