Frequency shift from speed and angle¶

See Longitudinal frequency shift from speed.

Notes:

It is not trivial to substitute moving source and idle observer with moving observer and idle source. Law depends on the current frame (observer or source are at rest at this frame), angle is detected at the point of emission or at the point of reception (see relativistic angle aberration).

Conditions:

Angle is measured at the moment of emission with respect to the observer frame.
Motion is in 2D space.

observer_frequency¶

Observed temporal_frequency of the wave.

Symbol:: f_o
Latex:: \(f_\text{o}\)
Dimension:: frequency

source_frequency¶

Source temporal_frequency of the wave.

Symbol:: f_s
Latex:: \(f_\text{s}\)
Dimension:: frequency

relative_speed¶

Relative speed between the source and the observer.

Symbol:: v
Latex:: \(v\)
Dimension:: velocity

source_angle¶

angle between the signal vector (directed from the source to the observer) and the source’s velocity vector.

Symbol:: phi
Latex:: \(\varphi\)
Dimension:: angle

law¶

f_o = f_s * sqrt(c^2 - v^2) / (c - v * cos(phi))

Latex:: \[f_\text{o} = \frac{f_\text{s} \sqrt{c^{2} - v^{2}}}{c - v \cos{\left(\varphi \right)}}\]