Dopplerformel

The Dopplerformel, also known as the Doppler equation, describes the change in frequency or wavelength of a wave in relation to an observer moving relative to the source of the wave. Named after the Austrian physicist Christian Doppler, this formula is fundamental in various fields such as astronomy, radar technology, and medical imaging.

The basic form of the Dopplerformel for waves propagating through a medium (such as sound) is expressed as:

f' = f × (v + v_o) / (v + v_s)

where:

- f' is the observed frequency,

- f is the emitted frequency,

- v is the speed of the wave in the medium,

- v_o is the velocity of the observer relative to the medium (+ if moving toward the source),

- v_s is the velocity of the source relative to the medium (+ if moving away from the observer).

For electromagnetic waves, such as light, the formula accounts for relativistic effects, especially when objects move at speeds close to the speed of light. The relativistic Dopplerformel is given by:

f' = f × sqrt((1 + β cos θ) / (1 - β cos θ))

where β = v / c (v being the relative velocity and c the speed of light), and θ is the angle between the wave's propagation direction and the relative motion.

The Dopplerformel has practical applications in astronomy for measuring stellar velocities, in radar systems for speed detection, and in medical ultrasound to observe blood flow. Its principles are fundamental in understanding wave behavior in moving frames of reference.