Relativistic Doppler Effect Calculator
Here’s a comprehensive table summarizing the key aspects of the Relativistic Doppler Effect:
| Aspect | Description |
|---|---|
| Definition | The change in frequency or wavelength of light due to relative motion between source and observer, accounting for special relativity effects134 |
| Formula (Frequency) | f′=f1−β1+βf′=f1+β1−β where $\beta = v/c$23 |
| Formula (Wavelength) | λ′=λ1+β1−βλ′=λ1−β1+β where $\beta = v/c$14 |
| Variables | $f’$ or $\lambda’$: Observed frequency or wavelength $f$ or $\lambda$: Source frequency or wavelength $v$: Relative velocity between source and observer $c$: Speed of light |
| Red Shift | Observed wavelength is longer when source moves away from observer3 |
| Blue Shift | Observed wavelength is shorter when source moves toward observer3 |
| Longitudinal Effect | Applies when source and observer move directly towards or away from each other4 |
| Transverse Effect | Applies when source and observer move perpendicular to the line of sight4 |
| Time Dilation | Incorporated in the relativistic formula, unlike classical Doppler effect4 |
| Lorentz Factor | $\gamma = \frac{1}{\sqrt{1 – \beta^2}}$, used in more complex scenarios4 |
| Arbitrary Direction | For motion at angle $\theta$: f′=fγ(1+βcosθ)f′=γ(1+βcosθ)f4 |
| Importance | Used in astronomy, cosmology, and particle physics34 |
| Difference from Classical | Includes special relativity effects and is independent of the medium4 |
This table provides a concise overview of the Relativistic Doppler Effect, including its formulas, key concepts, and applications. It’s important to note that the relativistic version differs from the classical Doppler effect by incorporating special relativity principles, making it more accurate for high-speed scenarios or astronomical observations.