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The Doppler effect is the change in frequency (pitch) of a wave when the source or observer is moving relative to the medium. A sound source moving toward you has a higher apparent frequency; moving away has lower frequency. Used in radar, medical ultrasound, and astronomy.

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1. 1Observed frequency: f_obs = f_source × (v + v_observer) / (v + v_source)
2. 2v = speed of sound (~343 m/s in air at 20°C)
3. 3v_source positive = moving away from observer; negative = moving toward
4. 4Redshift in astronomy: distant galaxies' light shifts to lower frequencies as they recede

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