What are doppler shifts at relativistic speeds?

Doppler shifts at relativistic speeds are like when a siren on a super-fast ambulance changes pitch as it zooms past you, but even faster and more extreme.

Imagine you're sitting on the curb, and a fire truck is whizzing by you so fast that it's almost like time is slowing down for you. When the truck comes toward you, its siren sounds higher, like when your brother runs up to you yelling "I won!", but when it zooms away, the sound gets lower, like when he walks off grumbling "I lost."

At relativistic speeds, things get even more wild. That fire truck isn’t just fast, it’s going close to the speed of light! So if it's coming toward you, its siren would sound super high, maybe like a tiny robot screaming, and when it zooms off, it would sound really low, almost like a sleepy turtle.

This change in pitch is called a Doppler shift. It happens because the waves from the source (like the fire truck’s siren) get squished or stretched depending on whether the source is moving toward you or away from you, just like when you play with waves in a bathtub!