The Doppler effect is the change in frequency or wavelength of a wave in relation to an observer moving relative to the source of the wave. It is most commonly observed with sound waves.
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The Doppler effect occurs when there is relative motion between a source of sound and an observer.
When the source of sound approaches the observer, the frequency appears higher (blue shift); when it moves away, the frequency appears lower (red shift).
The formula for the observed frequency $f' = f \left(\frac{v + v_o}{v - v_s}\right)$ where $f$ is the emitted frequency, $v$ is the speed of sound, $v_o$ is the velocity of the observer, and $v_s$ is the velocity of the source.
The Doppler effect has applications in radar and medical imaging technologies like ultrasound.
A sonic boom occurs when an object travels faster than the speed of sound, leading to a sudden change in pressure.