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

maths/special_numbers/perfect_number.py

@@ -25,6 +25,10 @@ def perfect(number: int) -> bool:
     Returns:
         True if the number is a perfect number, False otherwise.
 
+    Start from 1 because dividing by 0 will raise ZeroDivisionError.
+    A number at most can be divisible by the half of the number except the number
+    itself. For example, 6 is at most can be divisible by 3 except by 6 itself.
+
     Examples:
     >>> perfect(27)
     False
@@ -41,15 +45,35 @@ def perfect(number: int) -> bool:
     >>> perfect(8128)
     True
     >>> perfect(0)
-    >>> perfect(-3)
+    False
+    >>> perfect(-1)
+    False
     >>> perfect(12.34)
-    >>> perfect("day")
-    >>> perfect(["call"])
+    Traceback (most recent call last):
+      ...
+    ValueError: number must be an integer
+    >>> perfect("Hello")
+    Traceback (most recent call last):
+      ...
+    ValueError: number must be an integer
     """
+    if not isinstance(number, int):
+        raise ValueError("number must be an integer")
+    if number <= 0:
+        return False
     return sum(i for i in range(1, number // 2 + 1) if number % i == 0) == number
 
 
 if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()
     print("Program to check whether a number is a Perfect number or not...")
-    number = int(input("Enter number: ").strip())
+    try:
+        number = int(input("Enter a positive integer: ").strip())
+    except ValueError:
+        msg = "number must be an integer"
+        print(msg)
+        raise ValueError(msg)
+
     print(f"{number} is {'' if perfect(number) else 'not '}a Perfect Number.")

physics/doppler_frequency.py

@@ -0,0 +1,104 @@
+"""
+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()