Summarizing Doppler Effect and Sonic Booms

Summary

• The Doppler effect is an alteration in the observed frequency of a sound due to motion of either the source or the observer.
• The actual change in frequency is called the Doppler shift.
• A sonic boom is constructive interference of sound created by an object moving faster than sound.
• A sonic boom is a type of bow wake created when any wave source moves faster than the wave propagation speed.
• For a stationary observer and a moving source, the observed frequency \({f}_{\text{obs}}\) is:

  \({f}_{\text{obs}}={f}_{s}\left(\cfrac{{v}_{w}}{{v}_{w}±{v}_{s}}\right),\)

  where \({f}_{s}\) is the frequency of the source, \({v}_{s}\) is the speed of the source, and \({v}_{w}\) is the speed of sound. The minus sign is used for motion toward the observer and the plus sign for motion away.
• For a stationary source and moving observer, the observed frequency is:

  \({f}_{\text{obs}}={f}_{s}\left(\cfrac{{v}_{w}±{v}_{\text{obs}}}{{v}_{w}}\right),\)

  where \({v}_{\text{obs}}\) is the speed of the observer.

Glossary

Doppler effect

an alteration in the observed frequency of a sound due to motion of either the source or the observer

Doppler shift

the actual change in frequency due to relative motion of source and observer

sonic boom

a constructive interference of sound created by an object moving faster than sound

bow wake

V-shaped disturbance created when the wave source moves faster than the wave propagation speed