Question

How do you use a doppler equation?

Answer 1

Doppler effect:

1. Doppler effect or Doppler shift is a phenomenon that is observed whenever the source of waves is moving with respect to an observer.
2. The primary cause of the Doppler effect is the fact that, when the wave source moves in the direction of the observer, each successive wave crest that is generated by the source is emitted from a place that is closer to the observer.
3. As a result, the waves will now travel farther from the observer or arrive at wave crests more frequently as the source becomes closer and closer. This leads to an even greater increase in frequency.
4. Similar to this, when a wave source is moving away, the waves are emitted from a remote point, lengthening the time it takes for a new wave to arrive. As a result, there is a decrease in frequency.
5. Nevertheless, based on what we have learned thus far, we can conclude that a number of elements, including; the movement of the source and the observer, and the medium's movement.
   This generally applies to sound waves. In contrast, for waves that may propagate through any medium, like light, we just need to take into account the relative velocity differential between the source and the observer.
   1. The Doppler effect is the apparent change in frequency of a wave that occurs when the wave source, or the detector of the wave, is moving.
   2. Doppler effect is used in the range of medical tests using ultrasound to radar detectors and astronomy (with electromagnetic waves).
   3. The general formula of the Doppler Effect is given by,

$f^{\text{'}}=\left(\frac{{\displaystyle c\pm v_r}}{{\displaystyle c\pm v_s}}\right)f$.

Where,

$c$ is the propagation speed of waves in the medium,

$V_r=$ Speed of the receiver relative to the medium,

$V_r$ is positive if the receiver moves toward the source and negative if it moves in the opposite direction,

$V_S=$ Speed of the source relative to the medium,

$V_S$ is positive if the source moves away from the receiver and negative if it moves in the opposite direction,

$f$ is the frequency observed,

$f^{\text{'}}$ is the frequency emitted.

This how we can deduce the apparent frequency in the Doppler effect using the above equation.