A star is moving away from Earth at a speed of 2.4 ×10^8 m / s . Light of wavelength 480 nm is e

Name: Problem 57, Chapter 22: Physics
Uploaded: 2020-06-27T18:13:12-08:00
Duration: 1 min 30 s
Channel: Mayukh Banik
Description: A star is moving away from Earth at a speed of 2.4 ×10^8 m / s . Light of wavelength 480 nm is emitted by the star. What is the wavelength as measured by an Earth observer?

step 1 we have f0 equals f s 1 minus relative velocity over c 1 plus divided by 1 minus relative veloci

Question

A star is moving away from Earth at a speed of $2.4 \times 10^{8} \mathrm{m} / \mathrm{s} .$ Light of wavelength $480 \mathrm{nm}$ is emitted by the star. What is the wavelength as measured by an Earth observer?

   A star is moving away from Earth at a speed of $2.4 \times 10^{8} \mathrm{m} / \mathrm{s} .$ Light of wavelength $480 \mathrm{nm}$ is emitted by the star. What is the wavelength as measured by an Earth observer?

Physics

Alan Giambattista,… 2nd Edition

Chapter 22, Problem 57

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Solved by Expert Mayukh Banik

06/27/2020

Step 1

Step 1: We start with the formula for the Doppler effect for light, which is given by: \[\lambda_o = \lambda_s \sqrt{\frac{1 + \frac{v}{c}}{1 - \frac{v}{c}}}\] where: - $\lambda_o$ is the observed wavelength, - $\lambda_s$ is the source wavelength, - $v$ is Show more…

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A star is moving away from Earth at a speed of $2.4 \times 10^{8} \mathrm{m} / \mathrm{s} .$ Light of wavelength $480 \mathrm{nm}$ is emitted by the star. What is the wavelength as measured by an Earth observer?

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Key Concepts

Relativistic Doppler Effect

The relativistic Doppler effect describes the change in observed wavelength of light due to the relative motion between the source and observer at speeds close to the speed of light. Unlike the classical Doppler effect, it incorporates the effects of time dilation and requires the correct use of relativistic formulas to calculate the wavelength shift when the source is moving at a significant fraction of the speed of light.

Redshift

Redshift refers to the phenomenon where the observed wavelength of light is increased, or shifted towards the red end of the spectrum, when the light source is moving away from the observer. This effect is a direct consequence of the Doppler effect in a relativistic context and is used extensively in astronomy to measure the velocity of distant stars and galaxies.

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