Use of complex numbers to calculate Doppler effect?

1. How is the Doppler effect formula derived?
2. How do you calculate Doppler?
3. How do scientists measure distance with dopplers?

How is the Doppler effect formula derived?

Using the fact that the wavelength is equal to the speed times the period, and the period is the inverse of the frequency, we can derive the observed frequency: λo=λs+ΔxvTo=vTs+vsTsvfo=vfs+vsfs=v+vsfsfo=fs(vv+vs).

How do you calculate Doppler?

Doppler Effect Formula / Equation

V_r = speed of the receiver relative to the medium, +c if the receiver is moving towards the source, -c if the receiver is moving away. V_c = speed of the source relative to the medium, +c if the source is moving away -c if the source is moving towards the receiver.

How do scientists measure distance with dopplers?

The redshift phenomenon is a manifestation of the Doppler effect - the faster the motion, the larger the shift of the frequency. Therefore, the larger the redshift, the greater the distance to the observed galaxy. The exact relation between the redshift and distance follows from the cosmological model of the universe.