http://falstad.com/ripple/
See also this simple, but effective applet:
http://lectureonline.cl.msu.edu/~mmp/applist/doppler/d.htm
In this simulation, v/vs is the ratio of your speed to the speed of sound; e.g., 0.5 is you, or the blue dot, traveling at half the speed of sound. Note how the waves experienced on one side "pile up" (giving an observer a greater detected frequency, or BLUE SHIFT); on the other side, the waves are "stretched apart" (giving an observer a lower detected frequency, or RED SHIFT).
In astronomy, the red shift is very important historically: Edwin Hubble found that light from distant galaxies (as measured in their spectra) was red shifted, meaning that distant galaxies were moving away from us (everywhere we looked). The conclusion was obvious (and startling): The universe is expanding. Last year, local astrophysicist Adam Riess discovered that the rate of expansion was accelerating.
http://www.nobelprize.org/nobel_prizes/physics/laureates/2011/
It's worth noting that the effect also works in reverse. If you (the detector) move toward a sound-emitter, you'll detect a higher frequency. If you move away from a detector move away from a sound-emitter, you'll detect a lower frequency.
Mind you, these Doppler effects only happen WHILE there is relative motion between source and detector (you).
And they also work for light. In fact, the terms red shift and blue shift refer mainly to light (or other electromagnetic) phenomena.
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