A change in the frequency of a wave, often due to motion or modulation.A frequency shift is a change in the frequency of a wave, often caused by the relative motion between the source and observer (Doppler effect) or by time-varying modulation of the medium. This phenomenon is crucial in astronomy for detecting exoplanets, measuring the expansion of the universe, and studying the dynamics of stars and galaxies. In physics, frequency shifts also arise in nonlinear optics, gravitational wave detection, and quantum systems.
The Doppler effect was proposed by Christian Doppler in 1842 for sound waves and later applied to light by Hippolyte Fizeau. The gravitational redshift was predicted by Albert Einstein in 1916 as a consequence of general relativity.
When a wave source moves toward an observer, the observed frequency increases; when it moves away, the frequency decreases. The shift is proportional to the relative velocity along the line of sight. In general relativity, gravitational fields also cause frequency shifts: light climbing out of a gravitational well is redshifted. In modulated systems, such as a vibrating grating, the frequency of transmitted light can be shifted by the time-dependent phase modulation.
Frequency shifts are used in radar and lidar for speed measurement, in medical ultrasound for blood flow imaging, and in astronomy to measure stellar radial velocities and the cosmic microwave background dipole.
The most precise frequency shift measurements today can detect velocity changes of less than 1 millimeter per second, enabling the detection of Earth-sized exoplanets around nearby stars.

