Doppler Effect

Problem overview

The Doppler Effect, named after the Austrian physicist Christian Doppler, is a phenomenon in physics that describes the change in frequency or wavelength of a wave in relation to an observer moving relative to the source of the wave. In simpler terms, it explains why the sound or light from a moving object appears different to an observer compared to when the object is stationary.

I've also made little web demonstration (all gifs are from this demo), you can play with it here.

red = observer, gray = source

problem introduction

Looking at the gifs you can clearly see that observer "touches" waves with diffrent frequency. From these gifs it's also clearly seen that frequency depends on velocity of source and observer. It's important to note that we'll discuss only movement on the same axis (that means you can create displacement vector which always has the same direction).

Let's talk about what happens when observer is moving:

As we can see if observer is moving toward source, frequency is less than original one. When is moving away frequency is greater than original one. When observer is moving toward source, it is "crashing" with waves, but when is moving away, it is running away of them. The equations for an observer moving toward or away from a stationary source can be combined into one equation:
$$f_{o} = {V \pm V_{o} \over V}$$
where f_o is observed frequency, f_s is source' frequency, v is velocity of the wave and v_o is velocity of observer.
If observer is moving toward source, we're adding velocity, because frequency then is larger than original.
If observer is moving away of source, we're subtracting velocity, because frequency then is less than original.

Let's talk about what happens when source is moving:

As we can see if source is moving toward observer, frequency is greater than original one. When is moving away frequency is less than original one. When source is moving toward observer, waves of it are closer to each other, but when is moving away, they are away of each other. The equations for an source moving toward or away from a stationary source can be combined into one equation:
$$f_{o} = {V \over V \pm V_{s}}$$
where f_o is observed frequency, f_s is source' frequency, v is velocity of the wave and v_s is velocity of source.
If source is moving toward observer, we're subtracting velocity, because frequency then is larger than original.
If source is moving away of observer, w're adding velocity, because frequency then is less than original.

combined formula

When observer and source are moving at the same moment, we can combine 2 formulas into 1.

For the combined formula, rules are the same and formula looks like that: $$f_{o} = {V \pm V_{o} \over V \pm V_{s}}$$

Real life examples

You can observe doppler effect everyday. Most common example is passing car with some signal (honk, sirens or radio). You will note that you hear diffrent sound when it is closer to you and when it is approaching you.
Some radars uses doppler effect to detect objects. Objects simply bounces wave signal back which is detected then.

You can see my youtube playlist with some examples here.