Doppler shift
Measurement of current velocity using ADCP is based on the principle of Doppler shift. The Doppler effect (or the Doppler shift) is the change in frequency of a wave in relation to an observer who is moving relative to the wave source. A common example of Doppler shift is the change of pitch heard when a vehicle sounding a horn approaches and recedes from an observer.
The Doppler shift principle is used in ADCP to measure the speed and direction of water current velocities. The ADCP transducer elements emit a series of sound waves at a specific frequency. The echo is received by the ADCP system receiver and processed. The echo is received by the ADCP system receiver and processed. The Doppler effect will result in a frequency shift or a time dilation for the received echo. The frequency shift of the echoes reflected from the drifters is proportional to the speed of the water current.
Fd = 2Fs*(V/C)
•  Fd: The Doppler shift frequency [Hz].
•  Fs: Frequency of the transmitted sound waves from the ADCP transducer [Hz].
•  V: Relative velocity between the sound source and the sound receiver in the beam direction [m/s].
•  C: Sound speed [m/s]
Doppler shift may also be explained using time dilation. This means the changes to the signal in terms of time rather than frequency is proportional to the speed of the drifters. The echo from a pulse of sound transmitted towards a particle will look the same when the particle is still. If the particle moves away from the transmitter the distance it takes for the echo to travel back is a little longer for the end of the pulse compared to the start of the pulse. Thereby the received pulse is a stretched version of the transmitted. If the pulse is a sinusoidal, we will see that the stretching of the pulse has given it a lower frequency, a frequency shift.