How does the beat frequency change when the mirror's speed is much smaller than the speed of light?

AI Thread Summary
The discussion focuses on the calculation of beat frequency when a mirror is moving at a speed much smaller than the speed of light. The first part established the frequency of the reflected wave as f = f_source * (c + v) / (c - v). The second part requires demonstrating that the beat frequency can be expressed as f_beat = 2v / λ under the approximation that f + f_source ≈ 2f_source. The participant is struggling to find the correct approach, considering substituting f_source from the first part but finding it ineffective. Clarification on how to derive the beat frequency in this context is sought.
thenewbosco
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There are two parts to this but i solved the first part:
in part a) i was to show, for an electomagnetic wave reflected back to its source from a mirror approaching at speed v, that the reflected wave had frequency f=f_{source}\frac{c+v}{c-v} where fsource is the source frequency and c is the speed of light.

now i am asked: when v is much less than c, the beat frequency is much smaller than the transmitted frequency. In this case use the approximation f + f_{source}\approx 2f_{source} and show that the beat frequency can be written:

f_{beat}=\frac{2v}{\lambda}

i don't know how to go about this. I was thinking to solve for fsource and put it into the equation from part a. but this doesn't work...any help
 
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