# Doppler effect

Let’s assume that there is an insect in the center of a circular pool of water. The insect shakes its legs periodically to produce disturbances that travel through the water. If these disturbances originate at one point , then they would travel outward from that point in all directions at the same speed . The pattern produced by the trembling of the insect would be equal to a series of concentric circles , which would reach the edges of the pool of water at the same frequency. A person observing the left edge of the puddle would observe the disturbances at the same frequencythat an observer would observe at the right edge of the pool. This is basically the Doppler effect .

## What is the Doppler effect?

The Doppler effect is a physical phenomenon by means of which there is an apparent change in the frequencies of the waves that are presented by a sound source with respect to the observer of the same source that is in motion .

• What is the Doppler effect?
• History
• Types
• How does it work
• Formula
• Applications of the Doppler effect
• Experiments
• Relativistic Doppler effect
• Importance
• Examples of the Doppler effect

## What is the Doppler effect?

In order to understand the meaning of the Doppler effect we must understand some basic principles of physics and sound . In this aspect it is important to mention that sound is capable of traveling from one place to another by means of waves which do so at a fairly fast speed. This speed varies depending on the medium through which it travels and they have the ability to increase or decrease when they reach the ear. The Doppler effect , in addition to being related to sound, is also related to other types of waves. It consists then, in the changeof frequency having a waveform that is produced by the movement on the source that produces relative to its observer . It is a change in the apparent frequency of a wave produced by movement.

## History

Christian Doppler , a physicist and mathematician of Austrian origin, was the person who managed to describe the physical phenomenon that today we know as the Doppler effect , which he published in his monographic article on the colors of the light of double stars . Scientist Christoph Hendrik  also investigated the hypothesis in 1845 for sound waves by confirming that the pitch of a sound that is emitted by a source approaching the observer is sharper than if the source moves away. Hippolyte Fizeau conducted a series of experiments independently to study theelectromagnetic waves .

## Types

The types of Doppler effect that exist are the following:

• A moving observer : occurs when a source of rest emits waves of frequency propagating in the air so radial . To achieve determine the frequency measuring an observer is on or away from the source, shows that when the observer moves away from it, fronts come to him with a range more large than with which they were issued , as each front needs to travel an extra distance to reach the observer, the distance that the observer has traveled in the intervening time. So the observer measures a lower frequency when the observer moves away, and a higher frequency when he gets closer.
• A moving source : in this case the source is moving and the observer is at rest . Wave fronts are emitted from an advancing point, and accumulate while thinning out the rear. The result we obtain is a fixed observer in front of the transmitter , which measures a frequency of reception greater than that issuing, while one located behind measured less frequently.
• Both are in motion : it occurs when the source and the receiver are in motion with respect to the medium, the Doppler effect that results in this case is a combination of the previous two. To calculate it, what the emitter measures can be directly related to what the receiver measures , in this case, we would first obtain a Doppler effect due to a mobile source and a fixed observer , followed by one due to a fixed source and an observer. mobile .

## How does it work

The Doppler effect works as a variation of the frequency of a wave that is produced by a mobile with respect to a receiver that is in a static or moving place . It works because the source of the sound is in motion until it reaches the place where the receiver is.

## Formula

In order to evaluate the Doppler effect, there is a general formula that allows finding the frequency that the receiver or observer will perceive :

Where :

• f   =  refers to the frequency that the observer perceives (it is also used as  f   or frequency of the received signal)
• f   =  is the actual frequency emitted by the source (it is also used as  f   or frequency of the emitted signal)
• v   =  speed of sound (343 m / s)
• v   =  observer velocity (also used as  v   or receiver velocity)
• v   =  velocity of the source (also used as  v   or velocity of the emitter)

## Applications of the Doppler effect

One of the most important applications of the Doppler effect is that of radar , an electronic system that allows the detection of objects that cannot be observed with the naked eye and helps to determine their distance . Doppler radar measures the speed of objects such as a car or a ball, using a constant frequency . Another of its important applications is echocardiography , to carry out morphological and functional studies of the heart in healthy or sick individuals. This is achieved because this technique is based on theemission and reception of ultrasound , which has considerable advantages over other diagnostic procedures .

It is also used in the area of astrophysics allowing many important advances in the area, such as to determine the different structures of galaxies and the presence or absence of dark matter , it is also achieved through the Doppler effect to study the movements of the stars and galaxies .

## Experiments

We could perform the following experiment to test the Doppler effect:

A student with a speaker hooked up to a signal generator runs to a microphone and then walks away. As this happens, the sound that is picked up by the microphone is recorded and analyzed.

#### Materials

• Signal generator
• Speaker with a cable that is long enough
• Microphone
• Computer with Matlab and the Doppler Effect function

#### Description of the experiment

Connects the speaker to the signal generator via the cable and the signal generator is set so that the output frequency is 1000 Hz and the amplitude is high enough so that everyone can listen to the sound . The computer program generates a graph that results from the three situations: student at rest , student running towards the microphone, and student moving away from it.

## Relativistic Doppler effect

In the area of ​​physics we know as the relativistic Doppler effect the change that is observed in the frequency of light that comes from a source that is in relative motion with respect to the observer . The relativistic Doppler effect is different from the Doppler effect of other types of waves because the speed of light is constant for any observer regardless of their movement.

## Importance

The discovery of the Doppler effect was of the utmost importance at the beginning of the 20th century as it succeeded in showing that the universe is constantly expanding . In addition, it is used in many daily applications , and above all, in the field of medicine where many advances have been made in terms of diagnosis and treatment .

## Examples of the Doppler effect

Some examples of the Doppler effect are as follows:

When the siren of an ambulance sounds . Every time the sound is very far away and begins to approach, it is extremely sharp until it reaches us.

The radar of the Doppler type that are used by the Police of traffic to detect the direction and speed that approaches or moves away vehicle to determine whether circulating properly or if he commits an offense. This is obtained by means of the emission and reception of a radioelectric wave.