Doppler effect calculator (sound waves)

The Doppler effect is the change in perceived frequency of a wave (sound, light) caused by relative motion between source and observer. Discovered in 1842 by Christian Doppler.

As it approaches, sound waves are compressed (shorter wavelength, higher frequency). As it recedes they are stretched (longer wavelength, lower frequency). The observer hears this as a pitch change.

v_src > 0: source moving toward observer (frequency increase). v_src < 0: moving away (decrease). v_obs > 0: observer moving toward source (increase). v_obs < 0: moving away (decrease).

At v_src = v the denominator reaches zero and observed frequency goes to infinity. Physically a shock wave (sonic boom) forms. The calculator throws an error for v_src >= v.

343 m/s in air at 20 degrees C. Temperature-dependent: v = 331.3 * sqrt(1 + T/273.15) m/s. In water ~1480 m/s, in steel ~5000 m/s.

Yes, using the relativistic Doppler formula. Redshift (recession) was the key evidence for the expanding universe (Hubble 1929). Police radar also uses the Doppler effect.

Doppler ultrasound measures blood flow velocity. The transducer emits ultrasound; waves reflected from moving blood cells return at a shifted frequency. The difference indicates flow speed and direction.

Receding galaxies show redshift (spectral lines shift to lower frequencies). Approaching objects show blueshift. This allows measurement of stellar radial velocities to within 1 m/s precision.

Non-relativistic: v_radial = v_sound * (f_obs - f_src) / f_src. For light: v_radial ≈ c * delta_lambda / lambda. Measuring hydrogen line shifts gives approach/recession speeds of stars.

The formula is one-dimensional, valid when source and observer move along the same line. For motion at an angle a full 3D formula using the velocity component along the source-observer axis is required.