Doppler effect ( relationship between observed frequency and emitted frequency )

Description

The Doppler effect (or Doppler shift) is the change in frequency of a wave (or other periodic event) for an observer moving relative to its source. When the source of the waves is moving toward the observer, each successive wave crest is emitted from a position closer to the observer than the previous wave. Therefore, each wave takes slightly less time to reach the observer than the previous wave. Hence, the time between the arrival of successive wave crests at the observer is reduced, causing an increase in the frequency. When the observer is very close to the path of the object, the transition from high to low frequency is very abrupt. When the observer is far from the path of the object, the transition from high to low frequency is gradual. If the speed of the receiver relative to the medium and the velocity of the source relative to the medium are small compared to the speed of the wave, there is a relationship between observed frequency and emitted frequency.

Related formulas

Variables

fThe observed frequency (Hz)
f0The emitted frequency (Hz)
vrThe velocity of the receiver relative to the medium (positive if the receiver is moving towards the source and negative in the other direction) (m/s)
vsThe the velocity of the source relative to the medium ( positive if the source is moving away from the receiver and negative in the other direction) (m/s)
cThe velocity of waves in the medium (m/s)