added a function to calculate perceived frequency by observer using Doppler Effect

physics/doppler_frequency.py

@@ -0,0 +1,106 @@
+"""
+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.
+
+Now, 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.
+
+All these results are 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) #observer and source moving towards each other
+    106.25
+    >>> doppler_effect(100, 330, -10, -10) #observer and source moving away
+    94.11764705882354
+    >>> doppler_effect(100, 330, 10, 330) #source moving at the same speed as the wave
+    Error: Division by zero
+    Infinite frequency implies vs = v and observer infront of the source
+    0.0
+    >>> doppler_effect(100, 330, 10, 340) #source moving faster than the wave
+    Error: Non-positive frequency
+    Non-positive frequency implies vs > v or v0 > v(in opposite direction)
+    0.0
+    >>> doppler_effect(100, 330, -340, 10) #observer moving faster than the wave
+    Error: Non-positive frequency
+    Non-positive frequency implies vs > v or v0 > v(in opposite direction)
+    0.0
+    """
+
+    try:
+        doppler_freq = (org_freq * (wave_vel + obs_vel)) / (wave_vel - src_vel)
+    except ZeroDivisionError:
+        print("Error: Division by zero")
+        print("Infinite frequency implies vs = v and observer infront of the source")
+        return 0.0
+    if doppler_freq <= 0:
+        print("Error: Non-positive frequency")
+        print("Non-positive frequency implies vs > v or v0 > v(in opposite direction)")
+        return 0.0
+    return doppler_freq
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()