iframe-proxy | Sunbelt Computer Software

History

104 lines (87 loc) · 4.37 KB

Raw

100

101

102

103

104

"""

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()

Sunbelt Computer Software

PL/B Language Development and Support

Navigation Menu

Sunbelt Computer Software

PL/B Language Development and Support

FilesExpand file tree

doppler_frequency.py

Latest commit

History

doppler_frequency.py

File metadata and controls