# Doppler effect:

You are in a car when you start to hear the sound of an ambulance approaching. As the vehicle approaches yours, the sound of the siren becomes more and more acute. It passes close to you, and as it moves away, the sound of the siren becomes more serious as the distance increases. This is a classic example of the Doppler effect with sound waves.

If you want to better understand what this effect is, how it can happen, and what the formulas are that govern this physical event, continue reading this article. In addition to being interesting knowledge about everyday things, the topic usually appears in entrance exams, especially in specific second-phase tests or tests specific to exact sciences. So, read more!

## What is the Doppler effect?

In a scientific view, the Doppler effect is a wave phenomenon. It happens when the observer and the wave emission source are in motion towards each other, either because they are approaching or moving away.

Depending on how this locomotion occurs, the impression that the observer will have is that the frequency of the waves is increasing, with more undulations in the same period of time. Or, it may appear that the frequency is decreasing, with fewer waves in a given period of time.

It is important to remember that this phenomenon works with a wave appearance; that is, the source continues to emit exactly the same wave with the same characteristics of frequency, length, and propagation speed. What has changed is the observer’s perception of the movement in progress.

### Interpretation of the Doppler effect

In the animation above, notice that the black dot is moving in a horizontal direction, towards the right. Everything in front of it (on the right) has a higher apparent frequency, as you can see by the greater union between the different circles, which represent wave crests.

At the same time, the waves that are behind the direction of travel (to the left) appear to be further apart from each other. So, if they were sound waves, it means that the sound would be more serious for an observer located after the point.

This interpretation indicates that, when a wave source and the observer are approaching each other, the apparent frequency will be higher and, in the case of sounds, more acute. Otherwise, when there is distance between the two entities, the sound will be more serious, as the waves will be at a lower apparent frequency. Based on this, we will resolve the following question:

## Resolve the following question:

(PUCCAMP-SP) A teacher reads his newspaper sitting on a park bench and, paying attention to the sound waves, analyzes three events:

I – A car alarm goes off when the owner opens the trunk lid.

II – An ambulance approaches the square with its siren on.

III – A bad, impatient driver, after passing through the square, drives away with the horn permanently on.

The teacher notices the Doppler effect only:

a) in event I, with invariable sound frequency

b) in events I and II, with a decrease in frequency

c) in events I and III, with increased frequency

d) in events II and III, with a decrease in frequency in II and an increase in III

e) in events II and III, with an increase in frequency in II and a decrease in III

The Doppler effect will only be observed when movement occurs between the observer and the sound source. In event I there is no such locomotion, because both entities are stationary in space, so alternatives A, B and C can now be eliminated.

As we have seen, the proximity between source and observer is perceived as an increase in frequency, apparently. And, in the case of a separation, this perception is given by a decrease in frequency, with more serious sounds. So, event II will have an increase in frequency, while event III will have a lower apparent frequency as the car with the horn activated moves away. Therefore, the best alternative would be the letter E.

## Doppler effect formula

and f o = is the frequency perceived by the observer

f = is the real frequency emitted by the source

so tyhe v = wave speed in the medium, for the speed of sound in air v = c = 340 m/s

o = speed of the observer in space

f = source speed in space

When v o <0 it means that the observer and the source are moving away. Similarly, when v o >0 it is because the emitting source and observer are in proximity.

When v f >0 it is because the body that emits the waves is at a distance from the observer. On the other hand, if v f < 0, then the source is approaching the observer.

These signal variations make the Doppler effect formula very interpretive, with total dependence on the context presented. Let’s apply this knowledge with a question from Fundação Getúlio Vargas:

(FGV)

A car travels at 20 m/s on a straight road. The car approaches a person, stopped on the shoulder, wanting to cross the road. The car driver, to alert her, blows the horn, the sound of which he hears is 640 Hz. The frequency of the horn sound perceived by the stopped person is approximately