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Simuladores de Efeito Doppler

1)Estático

2) Dinâmico

 

 

 

Doppler Effect and the Cosmos

The Doppler Effect is observed in all kinds of waves , including electromagnetic waves like LIGHT. It has been observed in the light form stars. These observations led to the most astonishing discovery: the Universe is expanding! The light from most stars and galaxies arrive to our telescopes red-shifted. That means that the frequency of the original light has increased (moved towards the frequency of the red light, that is the lowest of visible light). In analogy with the ambulance example, we conclude that these stars and galaxies are moving away from us! The larger the red-shift, the larger the speed. It was discovered by E. Hubble (the astronomer , not the space telescope) that the faster the star, the larger its distance to us! There are, however, a few galaxies that move towards us. Their light is blue-shifted.

 

 

Efeito Doppler

Este é um efeito muito interessante e importante! Ele foi descoberto pelo físico Austríaco Christian Doppler em 1842 e tem sido crucial para a astrofísica e a cosmologia (leia texto à direita) e é também aplicado na medicina, aviação, etc... é também usado pelos golfinhos!

O exemplo típico é o som da sirene de uma ambulância, quando aproxima-se de você e depois passa e se distancia. A frequência do som que você ouve é mais alta quando a ambulância se aproxima a mais baixa quando ela se distancia. Essa variação da frequência, que resulta do movimento entre o emissor de som e o recipiente depende da velocidade entre estes: quanto maior esta velocidade, maior a variação de frequência. Isso ocorre com ondas sonoras e também com qualquer outro tipo de onda ( luz, ondas na água, etc.). Essa idéia é representada por uma fórmula bastante simples:

fr = frequencia recebida, fs = frequencia da fonte (emissor), v = velocidade da onda e vs = velocidade da fonte (é positiva quando fonte e recipiente se aproximam e negativa quando se distanciam)


It is expected a positive velocity when objects approach each other, because in that case the fraction will have a value larger then 1 and as a result fr > fs as you would expect. And vice-versa.

EXAMPLE

Let´s apply the formula above to the ambulance example. Suppose the ambulance is travelling towards you with a velocity of 50 m/s and emitting a 300 Hz sound. What sound frequency will you receive? (the speed of sound waves in air is 343 m/s)

Answer:

fs = 300 Hz, vs = 50 m/s, v = 343 m/s (important: the numbers must be in these units used here )

fr = (343 / 343-50) 300 = 1.17* 300 = 351 Hz

The following images will illustrate the concept of Doppler Effect.

Imagine water drops falling into a pond, so that you get those familiar ripples in the water (λ is the wavelength):

Any observer around will detect the same wavelength λ.

Now imagine that the source of the water drops start moving to the left, so that you will see that:

An observer at A detects a wavelength λ1 which is smaller than the wavelength λ2 detected by an observer at B. Remember that a smaller wavelength corresponds to a higher frequency.

λ1 < λ < λ2

This images were produced using my Doppler effect simulation, which you can also use. Try varying the velocity to obtain different patterns.

It is interesting to notice that the distance between the centres of the circular waves gives an idea of the velocity at which the wave source moves:

This image was produced using the static simulator. Play with it. Try different velocities for the wave source!

Bow Waves

If you have been playing with the Doppler effect simulators, you must be curious about what happens when you choose a high velocity.

If the velocity of the wave source is too high, it can be higher than the velocities of the waves it emits! In this case we get a cone shape:

That is what happens, for instance, when an aircraft breaks the sound barrier. Fighters can travel faster than the speed of sound and produce this kind of waves.

You can also see this V-shaped pattern when you observe the waves produced at the rear end of a motorboat.