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Amara

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[Note from mentor: this thread was originally posted in a non-homework forum, therefore it does not use the homework template.]

I have been given an equation for the relativistic doppler effect but I'm struggling to see this as a function and then give a first order Taylor expansion. Any help at all would be appreciated as I'm completely stuck.

fo/fs = √(1 + vrel/c) / √(1-vrel/c)

Where vrel is the relative speed of the source and the observer with respect to each other, c the speed of light, and vrel > 0 is here presumed to mean that the source and

the observer move towards each other. Consider the relativistic Doppler effect in the case of (vrel/c) ≪ 1, but (vrel/c) > 0. Write a first-order Taylor expansion for the relativistic Doppler effect, and show that the result is equivalent to either of the two expressions found for sound.

The expressions for sound are:

i) The source moves with speed vs towards stationary observer

fo/fs = 1 / (1-(vs/v))

ii) The observer moves with speed vo towards the stationary source

fo/fs = 1 + (vo/v)

I have been given an equation for the relativistic doppler effect but I'm struggling to see this as a function and then give a first order Taylor expansion. Any help at all would be appreciated as I'm completely stuck.

fo/fs = √(1 + vrel/c) / √(1-vrel/c)

Where vrel is the relative speed of the source and the observer with respect to each other, c the speed of light, and vrel > 0 is here presumed to mean that the source and

the observer move towards each other. Consider the relativistic Doppler effect in the case of (vrel/c) ≪ 1, but (vrel/c) > 0. Write a first-order Taylor expansion for the relativistic Doppler effect, and show that the result is equivalent to either of the two expressions found for sound.

The expressions for sound are:

i) The source moves with speed vs towards stationary observer

fo/fs = 1 / (1-(vs/v))

ii) The observer moves with speed vo towards the stationary source

fo/fs = 1 + (vo/v)

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