Intuitive explanation for why the Doppler effect (and red-shift) happens? I was looking for an intuitive explanation as to why the Doppler effect happens. I haven't found any, but this is what I thought:
-Waves emitted travel at a constant speed
-The source emits a wave
-If the source remained still, then in a given time, there would a large distance between the emitted wavefront and the stationary source
-But if the source starts moving, the speed of the source relative to the wavefront is higher.
-This means in a given time, the distance between the emitted wavefront and the source will be lower
-So when the source (while moving) emits a new wavefront, the distance between wavefronts will also be lower
Is this explanation wrong? It suggests that the Doppler effect with light will be barely noticeable, because even if a source starts moving, because the speed of light is so high, the source speed will still be small relatively, so there will be a small (basically insignificant) decrease in distance between wavefronts. So how can red-shift be so noticeable, unless recession speed is extremely high (so high that it is actually significant relative to the speed of light)?
Your intuition is correct - a moving source emitting wavefronts periodically will be closer to the previously emitted wave in the direction of motion, and farther from the previously emitted wave in the opposite direction - see the simulation here.
You are also correct that the size of the effect depends on the speed of the observer relative to the speed of the wave.  That is why we can easily experience the Doppler shift for sound in everyday life (e.g. the sound of a car when it is approaching vs. receding) but we never notice the Doppler shift for light.  The speed of sound is a lot slower, and thus a lot closer to the velocities of everyday life, so the effect is larger for sound.
While the shift for light is too small for our eyes to perceive (e.g. not enough to change an object’s perceived color), sensitive instruments can measure extremely small changes in wavelength.  For example, the spectrographs that astronomers use to make radial velocity measurements of stars for the purposes of detecting extrasolar planets (via the star’s motion as the planet orbits) can now routinely measure velocities with a precision of 1 m/s - a leisurely walking speed for a human!