Module 39: The Relativistic Doppler Effect - Problem 2
I derived the Relativistic Doppler Shift formula for light waves, and noted that the same formula has to apply to rates associated with a series of light flashes. Here, you’ll work that out explicitly. To that end, imagine that George is firing photons toward Gracie at a rate of photons per second. Imagine that Gracie is running toward George at a speed .
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1. Question
From George's perspective, what is the distance between each of the photons that are shooting toward Gracie?
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2. Question
From George's perspective, what is the time interval between Gracie receiving one photon and the next?
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3. Question
From George's perspective, how many photons does Gracie receive per second?
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4. Question
From Gracie's perspective, how many photons does George send out per second?
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5. Question
From Gracie's perspective, what is the distance between each successive photon that George fires?
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6. Question
According to Gracie what is the time interval between the arrival of successive photons?
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7. Question
According to Gracie, then, how many photons does she receive per second?