A change in the observed frequency of a wave due to relative motion between the source and observer is called Doppler Effect

For example when a police siren approaches us, we hear a high pitched (high frequency) sound and as the siren passes away from us, we hear a low pitched sound even though the siren produces the sound at the same frequency throughout.

So different observers note a different frequency for the same wave depending upon their relative motion with respect to the source.

We know that it is the relative motion between the source and the observer that results in Doppler shift. And we also know that motion is a relative thing, so whether it is the source or the observer who is moving, things should remain the same for the observer in both the scenarios.

In other words the observer will not be able to tell whether he is moving towards the source or the source is moving towards him because from his perspective both scenarios are identical. The implications of this are enormous, in case if the observer is able to tell who is actually moving by looking at a particular wave or projectile released by the source, then that obviously goes against the basic premise that motion is relative.

Imagine that a stationary source fires a projectile towards a stationary observer at 10m/s. The observer here obviously sees the projectile approaching him at velocity 10m/s. Now imagine the following two scenarios

1) the source moving at 10m/s towards the observer as it fires the projectile
2) the observer moving towards the source at 10m/s as the source fires the projectile

From the observer’s perspective he is always stationary and hence he notes no difference in the above scenarios, according to him, the source is approaching him at 10m/s and the projectile at 20m/s. He sees no difference in what he experiences and he will not be able to tell who is actually moving.

But how come an observer experiences a wave differently depending upon who is moving?