Frequency shift from speed in arbitrary 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.
Also see Frequency shift from speed in collinear motion.
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 speeds are much less than the speed of light, i.e. this law is non-relativistic.
- 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¶
Magnitude of the velocity vector of the source. See
speed.- Symbol:
v_s- Latex:
\(v_\text{s}\)
- Dimension:
velocity
- observer_speed¶
Magnitude of the velocity vector of the observer. See
speed.- Symbol:
v_o- Latex:
\(v_\text{o}\)
- Dimension:
velocity
- source_angle¶
anglebetween the wave velocity and the source velocity.- Symbol:
theta_s- Latex:
\(\theta_\text{s}\)
- Dimension:
angle
- observer_angle¶
anglebetween the wave velocity and the observer velocity.- Symbol:
theta_o- Latex:
\(\theta_\text{o}\)
- Dimension:
angle
- law¶
f_o = f_s * (v - v_o * cos(theta_o)) / (v - v_s * cos(theta_s))- Latex:
- \[f_\text{o} = \frac{f_\text{s} \left(v - v_\text{o} \cos{\left(\theta_\text{o} \right)}\right)}{v - v_\text{s} \cos{\left(\theta_\text{s} \right)}}\]