Derivation of Doppler speed measurement formula

Derivation process of mechanical wave Doppler formula

Reference articles for the derivation of the electromagnetic wave Doppler formula

1. Calculate the distance

In the process of Doppler speed measurement, the displacement is counted by wavelength (because the speed measurement process includes one round and one round, it needs ×2):

Because the phase of a cycle is 2 $\pi$ , so m is equal to the total phase divided by 2$p$ :

so:

=>

2. Calculation speed

Velocity is defined as the derivative of displacement with time:

3. Calculation of angular velocity

The commonly used angular velocity calculation formula is:

the definition formula of angular velocity is:

The calculation formula of frequency and speed can be obtained as follows: