Relativistic Doppler Effect Formula - Definition, Formula , Solved Examples
Relativistic Doppler Effect Formula : The Relativistic Doppler Effect is a fundamental concept in physics, helping us understand how the universe behaves at high speeds.
Murtaza Mushtaq11 Oct, 2023
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Relativistic Doppler Effect Formula : The Relativistic Doppler Effect is a relativistic correction to the classical Doppler Effect, which describes the change in frequency and wavelength of waves due to the relative motion of the source and observer. This effect comes into play when objects are moving at a substantial fraction of the speed of light.
The Relativistic Doppler Effect holds immense significance in modern physics and astrophysics. It accounts for the changes in frequency and wavelength of electromagnetic waves when objects move at significant fractions of the speed of light. This phenomenon is fundamental in understanding the behavior of light from distant cosmic objects, such as galaxies and stars, as they move relative to observers on Earth. The Relativistic Doppler Effect plays a critical role in confirming the expanding universe theory, enabling us to measure cosmic velocities and infer crucial information about the cosmos. Its applications also extend to technologies like GPS, where it corrects for satellite motion at high speeds, making it an indispensable tool in both theoretical and practical aspects of physics and navigation.Formula Of Relativistic Doppler Effect
The formula for the Relativistic Doppler Effect can be expressed as follows: f' = f * sqrt((1 + β) / (1 - β))Where:
- `f'` is the observed frequency. - `f` is the source frequency. - `β` is the ratio of the relative velocity to the speed of light.Alternatively
Also Check - Soil Erosion Formula
Solved Problems Of Relativistic Doppler Effect Formula :
Solved Problem 1: A spaceship is moving at 0.95c, and it detects a gamma-ray burst with a known frequency of 10^20 Hz. What is the observed frequency on the spaceship?Solution:
Using the Relativistic Doppler Effect formula, we calculate the observed frequency as follows: f' = f * sqrt((1 + β) / (1 - β)) f' = 10^20 Hz * sqrt((1 + 0.95) / (1 - 0.95)) f' ≈ 3.74 x 10^20 Hz So, the observed frequency on the spaceship is approximately 3.74 x 10^20 Hz.Also Check - Photon Energy Formula
Solved Problem 2: A galaxy is moving away from Earth at 0.7c, and it emits light with a wavelength of 500 nm. What is the observed wavelength on Earth?Solution:
Using the Relativistic Doppler Effect formula for wavelength, we have: λ' = λ * sqrt((1 - β) / (1 + β)) λ' = 500 nm * sqrt((1 - 0.7) / (1 + 0.7)) λ' ≈ 195.48 nm So, the observed wavelength on Earth is approximately 195.48 nm.Also Check - Shear Modulus Formula
Solved Problem 3: A rocket is moving towards a star at 0.6c, and the star emits radio waves at 1 GHz. What is the observed frequency on the rocket?Solution:
Using the formula, we can calculate the observed frequency: f' = f * sqrt((1 + β) / (1 - β)) f' = 1 GHz * sqrt((1 + 0.6) / (1 - 0.6)) f' ≈ 2.5 GHz The observed frequency on the rocket is approximately 2.5 GHz.Also Check - Efficiency Formula
Solved Problem 6:
An astronaut on a spaceship moving at 0.8c observes a laser emitting light at 600 nm. What is the observed wavelength?Solution:
Applying the Relativistic Doppler Effect formula for wavelength, we get: λ' = λ * sqrt((1 - β) / (1 + β)) λ' = 600 nm * sqrt((1 - 0.8) / (1 + 0.8)) λ' ≈ 194.38 nm The observed wavelength on the spaceship is approximately 194.38 nm. Solved Problem 4: A distant galaxy is receding from Earth at 0.9c, and it emits visible light with a wavelength of 550 nm. What is the observed wavelength on Earth? Solution: Using the formula for wavelength, we can find the observed wavelength: λ' = λ * sqrt((1 - β) / (1 + β)) λ' = 550 nm * sqrt((1 - 0.9) / (1 + 0.9)) λ' ≈ 99.50 nm The observed wavelength on Earth is approximately 99.50 nm. These solved problems illustrate the application of the Relativistic Doppler Effect formula in different scenarios, showcasing its importance in understanding how waves are affected by relative motion. The Relativistic Doppler Effect is a fundamental concept in physics, helping us understand how the universe behaves at high speeds. It provides insights into the fascinating world of relativistic corrections to wave phenomena and plays a vital role in astrophysics and other scientific fields.The Relativistic Doppler Effect plays a critical role in confirming the expanding universe theory, enabling us to measure cosmic velocities and infer crucial information about the cosmos.Relativistic Doppler Effect Formula FAQs
What is the classical Doppler Effect?
The classical Doppler Effect describes the change in frequency or wavelength of waves due to relative motion, typically at much lower speeds than the speed of light.
Why is it called the 'Relativistic' Doppler Effect?
It's named 'relativistic' because it accounts for relativistic effects, considering objects moving at significant fractions of the speed of light.
How does the Relativistic Doppler Effect affect space observations?
It's crucial for astrophysicists as it explains the observed shifts in the spectra of distant galaxies and their motion.
Can the Relativistic Doppler Effect be applied to sound waves?
No, it's specific to electromagnetic waves, like light. Sound waves operate differently.
Can the Relativistic Doppler Effect be observed in everyday life?
Not in everyday scenarios, as the speeds involved are usually negligible compared to the speed of light.
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