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The Doppler Effect occurs because any energy waves – sound, light, water ripples, seismic waves, et al. – travel at a specific velocity dependent on the characteristics of the medium they are traveling through.
If both the source and observer are stationary with respect to the medium, the emitted and the observed frequencies are the same. If either of them are moving, the observed frequency is altered – with the waves being squeezed together in the direction of motion and stretched apart in the opposite direction. If it’s the source that’s moving, the waves in the medium are actually squeezed together (or stretched). If it’s the observer that’s moving, they only perceive them to be. But the effect on the observed frequency is the same.
If the source is moving through the medium at a velocity equal to or greater then the wave’s velocity, the waves in front of it get piled up directly on top of each other, creating a shock wave. You can see this in the bow wave of a boat, or hear it as a “sonic boom” from a jet.
Start with sound – light is a bit more complicated. Suppose you have a sound wave at a constant frequency hence wavelength moving from its source out to some place where you hear it. Let’s say it is the note A at 440 Hz. Now suppose you run toward the source of the sound. You’ll notice the pitch (frequency) increases. THe reason is your relative motion is making you encounter the subsequent wavelengths a little faster than that if you were standing still. Think of the crests and troughs being “fixed” in space so that as you run toward their source, you pass the crests and troughs in a shorter time than if you were standing still. Hence the wavelength appears shorter and the frequency higher. If you run away from the source, the wavelength appears longer hence the frequency lower.
It is slightly more complicated with light – the formula is the same but for light the shifting is really all about conservation of energy. The argument is slightly different than the one above but the net result is the same.
Perception of wavelength varies depending upon the relative velocity of the perceiver and the perceived.
Thus a train whistle has a higher pitch as it approaches than it does when it recedes.
Same applies to light, “red shift” from receding light sources, blue shift from approaching light sources.