# Relativistic Doppler Effect - Arbitrary Velocity

• unscientific
In summary, the observed frequency ##\nu## can be found in terms of proper frequency ##\nu_0##, speed ##v##, and radial velocity component ##v_r## for a source moving at velocity ##\vec v## with respect to the observer. For an observer in frame S, where the source is moving at speed ##\vec v## along the x-axis and at ##y=y_0##, the energy detected can be expressed in terms of ##E_0## and ##|v|## as ##E = \gamma E_0 = \frac{E_0}{\sqrt{1 - \frac{v^2}{c^2}}}##. This differs from the non-rel
unscientific

## Homework Statement

Find the observed frequency ##\nu## in terms of proper frequency ##\nu_0##, speed ##v## and radial velocity component ##v_r## for a source moving at velocity ##\vec v## with respect to the observer.

Now consider an observer in frame S where the source is seen moving at speed ##\vec v## along x-axis and at ##y=y_0##. At ##t=0##, the source is seen to emit frequency in ##-\hat y## direction. Find energy detected by the observer in terms of ##E_0## and ##|v|##.

## The Attempt at a Solution

Part(a)
Not sure how to approach this part. We've always done problems in standard configuration..

Part (b)

$$\nu = \gamma \nu_0$$
$$E = \gamma E_0 = \frac{E_0}{\sqrt{1 - \frac{v^2}{c^2}}}$$

Is this too easy to be true?

That's right. If you think about it, this differs from the non-relativistic Doppler shift because at t=0, the source isn't moving toward or away from the observer, yet you still see a change in frequency.

vela said:
That's right. If you think about it, this differs from the non-relativistic Doppler shift because at t=0, the source isn't moving toward or away from the observer, yet you still see a change in frequency.

Yeah I thought so too, it's just a manifestation of time dilation (which is independent of how far you are away in the non-general relativity context).

Any tips on part (a)?

bumpp

## 1. What is the Relativistic Doppler Effect?

The Relativistic Doppler Effect is a phenomenon in which the frequency and wavelength of electromagnetic waves (such as light) appear to be shifted when measured by an observer moving at a significant fraction of the speed of light.

## 2. How is the Relativistic Doppler Effect different from the classical Doppler Effect?

The classical Doppler Effect only takes into account the relative motion between the source of the waves and the observer, while the Relativistic Doppler Effect also considers the effects of time dilation and length contraction due to the observer's high velocity.

## 3. Can the Relativistic Doppler Effect be observed in everyday life?

Yes, the Relativistic Doppler Effect can be observed in everyday life, especially in situations where there is high relative motion between the source of the waves and the observer, such as in astronomy and in the study of cosmic rays.

## 4. How does the Relativistic Doppler Effect affect the perception of color?

The Relativistic Doppler Effect can cause a shift in the perceived color of an object due to the change in frequency and wavelength of the waves. This effect is known as "relativistic beaming" and is commonly observed in objects moving at high speeds, such as stars and galaxies.

## 5. Is the Relativistic Doppler Effect limited to electromagnetic waves?

No, the Relativistic Doppler Effect can also be observed in other types of waves, such as sound waves. In these cases, the effect is known as the "relativistic Doppler shift" and is caused by the same principles of time dilation and length contraction as in the electromagnetic case.

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