Doppler effect or Doppler shift is a phenomenon that is observed whenever the source of waves is moving with respect to an observer. For example, an ambulance crossing you with its siren blaring is a common physical demonstration of the Doppler Effect. In this article, let us understand the intricacies of the Doppler effect in detail.
Doppler Effect Explained
Doppler effect is an important phenomenon in various scientific disciplines, including planetary science. The Doppler effect or the Doppler shift describes the changes in the frequency of any sound or light wave produced by a moving source with respect to an observer.
Doppler effect in physics is defined as the increase (or decrease) in the frequency of sound, light, or other waves as the source and observer move towards (or away from) each other.
Waves emitted by a source travelling towards an observer gets compressed. In contrast, waves emitted by a source travelling away from an observer get stretched out. Christian Johann Doppler first proposed the Doppler Effect (Doppler Shift) in 1842.
Which person hears the sound of the revving engine with a greater magnitude?
Person A hears the sound of the revving engine with a greater magnitude than person B. Person B, standing behind the car, receives fewer waves per second (because they’re spread out), resulting in a low-pitched sound. But, person A who is in front of the car, receives more of those soundwave ripples per second. As a result, the frequency of the waves is higher, which means the sound has a higher pitch.
Case 2: Now let us consider the following situations:
Situation 1: How is the pattern of waves formed when you suddenly jump into a pond?
Situation 2: How is the pattern of waves formed when you are walking in a pond?
The difference in the wave pattern is due to the source’s movement in the second case. This is what the Doppler effect is. In the Doppler effect, the frequency received by the observer is higher during the approach, identical when the relative positions are the same, and keeps lowering on the recession of source.
Doppler Effect Formula
Doppler effect is the apparent change in the frequency of waves due to the relative motion between the source of the sound and the observer. We can deduce the apparent frequency in the Doppler effect using the following equation:
While there is only one Doppler effect equation, the above equation changes in different situations depending on the velocities of the observer or the source of the sound. Let us see below how we can use the equation of the Doppler effect in different situations.
(a) Source Moving Towards the Observer at Rest
In this case, the observer’s velocity is zero, so vo is equal to zero. Substituting this into the Doppler effect equation above, we get the equation of the Doppler effect when a source is moving towards an observer at rest as:
(b) Source Moving Away from the Observer at Rest
Since the velocity of the observer is zero, we can eliminate vo from the equation. But this time, the source moves away from the observer, so its velocity is negative to indicate the direction. Hence, the equation now becomes as follows:
(c) Observer Moving Towards a Stationary Source
In this case, vs will equal to zero, hence we get the following equation:
(d)Observer Moving Away from a Stationary Source
Since the observer is moving away, the velocity of the observer becomes negative. So, instead of adding vo, we now subtract, since vo is negative.
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