Derivation of Relativistic Doppler Shift: Step-by-Step Guide

In summary, the derivation of the relativistic doppler shift can be found in the book of Serway, but it is not in detail and step by step. There is a step from equation 1.13 to 1.14 which involves the formula 1 - (v^2/c^2) = (1 - v/c)(1 + v/c). The question was about how this resulted in a square root in the denominator of equation 1.14. The issue has been resolved.
  • #1
applied ahmed
3
1
i need thee the derivation of relativistic doppler shift. i found its derivation in the book of Serway, but it is not in detail and step by step.
in the book there is given that:
upload_2015-5-16_18-30-48.png


can anyone give me the step after eq#1.13? how eq#1.13 converted in the form of eq#1.14?
 
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  • #2
The step from 1.13 to 1.14 is just ## 1-\frac{v^2}{c^2}=(1- \frac{v}{c})(1+ \frac{v}{ c}) ##
 
  • #3
wabbit said:
The step from 1.13 to 1.14 is just ## 1-\frac{v^2}{c^2}=(1- \frac{v}{c})(1+ \frac{v}{ c}) ##
but how comes a square root in the denominator of eq#1.14
 
  • #4
thanks my problem solved
 
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Likes wabbit

Related to Derivation of Relativistic Doppler Shift: Step-by-Step Guide

1. What is the Relativistic Doppler Shift?

The Relativistic Doppler Shift refers to the change in the frequency of electromagnetic waves (such as light or radio waves) due to the relative motion between the source of the waves and the observer. This effect is described by the theory of relativity, which states that the observed frequency will be different for an observer in motion compared to an observer at rest.

2. Why is understanding the Relativistic Doppler Shift important?

Understanding the Relativistic Doppler Shift is important in various fields, such as astronomy, telecommunications, and satellite communication. It allows us to accurately measure the motion of objects in space, determine the speed of stars and galaxies, and ensure efficient communication between satellites and ground stations.

3. How is the Relativistic Doppler Shift derived?

The Relativistic Doppler Shift is derived using the principles of special relativity, which describe the relationship between space and time in the presence of relative motion. The derivation involves using the Lorentz transformation equations to calculate the change in frequency of the waves due to the relative velocity between the source and the observer.

4. What is the formula for the Relativistic Doppler Shift?

The formula for the Relativistic Doppler Shift is given by fobs = fsource * √((1+v/c)/(1-v/c)), where fobs is the observed frequency, fsource is the source frequency, v is the relative velocity between the source and the observer, and c is the speed of light.

5. How does the Relativistic Doppler Shift differ from the Classical Doppler Shift?

The Relativistic Doppler Shift takes into account the effects of special relativity, such as time dilation and length contraction, whereas the Classical Doppler Shift assumes that time and space are absolute and do not change with relative motion. Additionally, the Classical Doppler Shift is only accurate for relatively low velocities, while the Relativistic Doppler Shift is applicable for all velocities, including those close to the speed of light.

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