Frequency shift from speed in collinear motion¶
The Doppler effect or Doppler shift is the apparent change in frequency of a wave in relation to an observer moving relative to the wave source.
Notes:
When the source is moving with speed equal to wave speed, the observed frequency goes to infinity. This effect is known as the sonic boom.
Conditions:
The source and observer speeds are less or equal to the wave speed. Otherwise emitted waves are left behind the source or never reach the observer.
The source and observer are moving directly towards or away from each other (collinear motion).
Links:
- observed_frequency¶
Observed
temporal_frequencyof the wave.- Symbol:
f_o- Latex:
\(f_\text{o}\)
- Dimension:
frequency
- source_frequency¶
Wave
temporal_frequencyof the source.- Symbol:
f_s- Latex:
\(f_\text{s}\)
- Dimension:
frequency
- wave_speed¶
phase_speedof the wave.- Symbol:
v- Latex:
\(v\)
- Dimension:
velocity
- source_speed¶
speedof the wave source, positive when moving away from the observer and negative otherwise.- Symbol:
v_s- Latex:
\(v_\text{s}\)
- Dimension:
velocity
- observer_speed¶
speedof the observer, positive when moving away from the source and negative otherwise.- Symbol:
v_o- Latex:
\(v_\text{o}\)
- Dimension:
velocity
- law¶
f_o = f_s * (v - v_o) / (v + v_s)- Latex:
- \[f_\text{o} = \frac{f_\text{s} \left(v - v_\text{o}\right)}{v + v_\text{s}}\]