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

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Discussion Overview

The discussion revolves around the derivation of the relativistic Doppler shift, specifically focusing on the transition between two equations referenced as eq#1.13 and eq#1.14 from a textbook. Participants seek a detailed, step-by-step explanation of this derivation.

Discussion Character

  • Homework-related

Main Points Raised

  • One participant requests a detailed derivation of the relativistic Doppler shift, specifically asking for clarification on the transition from eq#1.13 to eq#1.14.
  • Another participant provides a mathematical identity stating that ## 1-\frac{v^2}{c^2}=(1- \frac{v}{c})(1+ \frac{v}{ c}) ## as part of the derivation process.
  • A subsequent participant questions how a square root appears in the denominator of eq#1.14, indicating a need for further clarification on this step.
  • One participant expresses satisfaction, stating that their problem has been solved, though it is unclear if this resolution addresses the earlier questions fully.

Areas of Agreement / Disagreement

The discussion does not present a consensus, as participants are still seeking clarification on specific steps in the derivation, particularly regarding the appearance of the square root in eq#1.14.

Contextual Notes

The discussion lacks detailed explanations of the assumptions or definitions involved in the derivation, and the mathematical steps leading to eq#1.14 remain unresolved.

applied ahmed
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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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The step from 1.13 to 1.14 is just ## 1-\frac{v^2}{c^2}=(1- \frac{v}{c})(1+ \frac{v}{ c}) ##
 
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
 
thanks my problem solved
 
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