One discovery that is used in a variety of ways is the Doppler effect, even though at first glance the scientific discovery would seem to be rather impractical.
The Doppler effect is all about waves, the things that produce those waves (sources), and the things that receive those waves (observers). It basically says that if the source and observer are moving relative to each other, then the frequency of the wave will be different for the two of them. This means that it's a form of scientific relativity.
There are actually two main areas where this idea has been leveraged into a practical outcome, and both have ended up with the handle of "Doppler radar." Technically, Doppler radar is what is used by police officer "radar guns" to determine the speed of a motor vehicle. Another form is the Pulse-Doppler radar which is used to track the speed of weather precipitation, and usually, people know the term from it being used in this context during weather reports.
Doppler Radar: Police Radar Gun
Doppler radar works by sending a beam of electromagnetic radiation waves, tuned to a precise frequency, at a moving object. (You can use Doppler radar on a stationary object, of course, but it's fairly uninteresting unless the target is moving.)
When the electromagnetic radiation wave hits the moving object, it "bounces" back toward the source, which also contains a receiver as well as the original transmitter. However, since the wave reflected off of the moving object, the wave is shifted as outlined by the relativistic Doppler effect.
Basically, the wave that is coming back toward the radar gun is treated as an entirely new wave, as if it were emitted by the target it bounced off of. The target is basically acting as a new source for this new wave. When it is received at the gun, this wave has a frequency different from the frequency when it was originally sent toward the target.
Since the electromagnetic radiation was at a precise frequency when sent out and is at a new frequency upon its return, this can be used to calculate the velocity, v, of the target.
Pulse-Doppler Radar: Weather Doppler Radar
When watching the weather, it is this system which allows for the swirling depictions of weather patterns and, more importantly, detailed analysis of their movement.
The Pulse-Doppler radar system allows not only the determination of linear velocity, as in the case of the radar gun, but also allows for the calculation of radial velocities. It does this by sending pulses instead of beams of radiation. The shift not only in frequency but also in carrier cycles allows one to determine these radial velocities.
In order to achieve this, careful control of the radar system is required. The system has to be in a coherent state which allows for stability of the phases of the radiation pulses. One drawback to this is that there is a maximum speed above which the Pulse-Doppler system cannot measure radial velocity.
To understand this, consider a situation where the measurement causes the phase of the pulse to shift by 400 degrees. Mathematically, this is identical to a shift of 40 degrees, because it has gone through an entire cycle (a full 360 degrees). Speeds causing shifts such as this are called the "blind speed." It is a function of the pulse repetition frequency of the signal, so by altering this signal, meteorologists can prevent this to some degree.
Edited by Anne Marie Helmenstine, Ph.D.