AAAAAAAAAAAAEEEEEEOOOOOOOOO

Have you ever wondered why the note of a train's horn moving past you goes from sharp to flat, like a pubescent choir boy struggling with a plagal cadence? (Sorry Ms. Pecko, I should have stuck to the drums)

Turns out, it has a much more succinct name: The Doppler effect.

Neat! So, what is the Doppler effect exactly?
Here's how Sheldon from TBBT explains it:


(eerie when it stops before the canned laughter, eh?)

"It's the apparent change in the frequency of a wave caused by relative motion between the source of the wave and the observer."

Those were a lot of words in 6 seconds. Let's break it down by going back to the train example. 

Imagine standing at a railroad crossing and listening to the train's horn. As the train gets closer to you, the pitch of the horn is higher. As it passes you and moves further away, the pitch becomes lower. From this, we can deduce that there is a relationship between the velocity of the wave source (with respect to you) and the frequency of the sound waves. 

This is the Doppler effect in a nutshell, and it applies to all waves. (Including light!)

     

Here are three really neat gifs that demonstrate the principle. (From Wikimedia Commons)

Referring to the three animations above, we can see that waves are compressed in front of a wave emitting object when it is in motion. In the opposite direction of the objects movement, we see that the pulses are spaced further apart, resulting in longer wavelengths. The faster an object is moving, the more compressed/elongated the emitted waves become. The rightmost image depicts an object breaking the sound-barrier, where all waves become bunched up in front of the object. This means that an observer would not hear any activity until the object passes them. 

This principle becomes especially useful when dealing with light. You see, light is wave too. On the longer end of our visible spectrum are the colors orange and red, while blue and violet sit on the shorter (higher energy) side of the spectrum. We can use this information to our advantage to determine whether something is moving towards or away from us, if we know what wavelength of light the object is supposed to be emitting. 

Two common terms used to describe such observations are redshift and blueshift.
As the following diagram demonstrates, blueshift occurs in the compressed area in the direction of motion of the light source. Redshift occurs in the elongated area following a light source in motion.

This nifty diagram shows the Doppler Effect in relation to light 

(From physics.ucr.edu - Jose Wudka)

In astronomy, the Doppler effect is extremely useful for finding the velocity of an object. If the frequency at the source is known, the observed frequency can be used to find the velocity of the source. 

We can use the following formula to calculate the speed at which something is moving if we know the resting wavelength and the observed wavelength of an object.

where lambda represents the wavelength emitted by the object

& c is the speed of light.