mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-22 11:10:14 +00:00
105 lines
4.4 KiB
Python
105 lines
4.4 KiB
Python
|
"""
|
||
|
Doppler's effect
|
||
|
|
||
|
The Doppler effect (also Doppler shift) is the change in the frequency of a wave in
|
||
|
relation to an observer who is moving relative to the source of the wave. The Doppler
|
||
|
effect is named after the physicist Christian Doppler. A common example of Doppler
|
||
|
shift is the change of pitch heard when a vehicle sounding a horn approaches and
|
||
|
recedes from an observer.
|
||
|
|
||
|
The reason for the Doppler effect is that when the source of the waves is moving
|
||
|
towards the observer, each successive wave crest is emitted from a position closer to
|
||
|
the observer than the crest of the previous wave. Therefore, each wave takes slightly
|
||
|
less time to reach the observer than the previous wave. Hence, the time between the
|
||
|
arrivals of successive wave crests at the observer is reduced, causing an increase in
|
||
|
the frequency. Similarly, if the source of waves is moving away from the observer,
|
||
|
each wave is emitted from a position farther from the observer than the previous wave,
|
||
|
so the arrival time between successive waves is increased, reducing the frequency.
|
||
|
|
||
|
If the source of waves is stationary but the observer is moving with respect to the
|
||
|
source, the transmission velocity of the waves changes (ie the rate at which the
|
||
|
observer receives waves) even if the wavelength and frequency emitted from the source
|
||
|
remain constant.
|
||
|
|
||
|
These results are all summarized by the Doppler formula:
|
||
|
|
||
|
f = (f0 * (v + v0)) / (v - vs)
|
||
|
|
||
|
where:
|
||
|
f: frequency of the wave
|
||
|
f0: frequency of the wave when the source is stationary
|
||
|
v: velocity of the wave in the medium
|
||
|
v0: velocity of the observer, positive if the observer is moving towards the source
|
||
|
vs: velocity of the source, positive if the source is moving towards the observer
|
||
|
|
||
|
Doppler's effect has many applications in physics and engineering, such as radar,
|
||
|
astronomy, medical imaging, and seismology.
|
||
|
|
||
|
References:
|
||
|
https://en.wikipedia.org/wiki/Doppler_effect
|
||
|
|
||
|
Now, we will implement a function that calculates the frequency of a wave as a function
|
||
|
of the frequency of the wave when the source is stationary, the velocity of the wave
|
||
|
in the medium, the velocity of the observer and the velocity of the source.
|
||
|
"""
|
||
|
|
||
|
|
||
|
def doppler_effect(
|
||
|
org_freq: float, wave_vel: float, obs_vel: float, src_vel: float
|
||
|
) -> float:
|
||
|
"""
|
||
|
Input Parameters:
|
||
|
-----------------
|
||
|
org_freq: frequency of the wave when the source is stationary
|
||
|
wave_vel: velocity of the wave in the medium
|
||
|
obs_vel: velocity of the observer, +ve if the observer is moving towards the source
|
||
|
src_vel: velocity of the source, +ve if the source is moving towards the observer
|
||
|
|
||
|
Returns:
|
||
|
--------
|
||
|
f: frequency of the wave as perceived by the observer
|
||
|
|
||
|
Docstring Tests:
|
||
|
>>> doppler_effect(100, 330, 10, 0) # observer moving towards the source
|
||
|
103.03030303030303
|
||
|
>>> doppler_effect(100, 330, -10, 0) # observer moving away from the source
|
||
|
96.96969696969697
|
||
|
>>> doppler_effect(100, 330, 0, 10) # source moving towards the observer
|
||
|
103.125
|
||
|
>>> doppler_effect(100, 330, 0, -10) # source moving away from the observer
|
||
|
97.05882352941177
|
||
|
>>> doppler_effect(100, 330, 10, 10) # source & observer moving towards each other
|
||
|
106.25
|
||
|
>>> doppler_effect(100, 330, -10, -10) # source and observer moving away
|
||
|
94.11764705882354
|
||
|
>>> doppler_effect(100, 330, 10, 330) # source moving at same speed as the wave
|
||
|
Traceback (most recent call last):
|
||
|
...
|
||
|
ZeroDivisionError: Division by zero implies vs=v and observer in front of the source
|
||
|
>>> doppler_effect(100, 330, 10, 340) # source moving faster than the wave
|
||
|
Traceback (most recent call last):
|
||
|
...
|
||
|
ValueError: Non-positive frequency implies vs>v or v0>v (in the opposite direction)
|
||
|
>>> doppler_effect(100, 330, -340, 10) # observer moving faster than the wave
|
||
|
Traceback (most recent call last):
|
||
|
...
|
||
|
ValueError: Non-positive frequency implies vs>v or v0>v (in the opposite direction)
|
||
|
"""
|
||
|
|
||
|
if wave_vel == src_vel:
|
||
|
raise ZeroDivisionError(
|
||
|
"Division by zero implies vs=v and observer in front of the source"
|
||
|
)
|
||
|
doppler_freq = (org_freq * (wave_vel + obs_vel)) / (wave_vel - src_vel)
|
||
|
if doppler_freq <= 0:
|
||
|
raise ValueError(
|
||
|
"Non-positive frequency implies vs>v or v0>v (in the opposite direction)"
|
||
|
)
|
||
|
return doppler_freq
|
||
|
|
||
|
|
||
|
if __name__ == "__main__":
|
||
|
import doctest
|
||
|
|
||
|
doctest.testmod()
|