Doppler Effect Question

[clothcut]

From AAMC4, q 10

A stationary receiver detects a change in frequency of a jet flying away from it at 300 m/s. Which of the following receivers will detect the same change in frequency from a jet flying away at 600 m/s

Answer: a receiver flying in 300 m/s the same direction of the jet.

I understand this if I draw a picture, but how is that derived from the doppler equation?? I tried using this:

f' = f (v +vo)/(v + vs)

for first case, f' = f (v)/(v + 300).... in the answer choice they give f' = f (v + 300)/(v + 600)... if these give the same shift, then why is it that if i try to plug in random values for f and v that they don't give me the same change in frequency (f')??

thanks

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[MedGrl@2022]

From AAMC4, q 10

A stationary receiver detects a change in frequency of a jet flying away from it at 300 m/s. Which of the following receivers will detect the same change in frequency from a jet flying away at 600 m/s

Answer: a receiver flying in 300 m/s the same direction of the jet.

I understand this if I draw a picture, but how is that derived from the doppler equation?? I tried using this:

f' = f (v +vo)/(v + vs)

for first case, f' = f (v)/(v + 300).... in the answer choice they give f' = f (v + 300)/(v + 600)... if these give the same shift, then why is it that if i try to plug in random values for f and v that they don't give me the same change in frequency (f')??

thanks

For all the AAMC practice exams I have found the equations for the doppler equation to be useless... just know it intuitively... I still have AAMC 8-11 to take.... so I will let you know if anything changes...

 

[mehc012]

From AAMC4, q 10

A stationary receiver detects a change in frequency of a jet flying away from it at 300 m/s. Which of the following receivers will detect the same change in frequency from a jet flying away at 600 m/s

Answer: a receiver flying in 300 m/s the same direction of the jet.

I understand this if I draw a picture, but how is that derived from the doppler equation?? I tried using this:

f' = f (v +vo)/(v + vs)

for first case, f' = f (v)/(v + 300).... in the answer choice they give f' = f (v + 300)/(v + 600)... if these give the same shift, then why is it that if i try to plug in random values for f and v that they don't give me the same change in frequency (f')??

thanks

That's actually a great observation...I instinctively said "one with the same relative velocity" but technically that's not true given the Doppler equation. Was it at least the closest answer out of the options given? Would have been nice if it were phrased "which of the following receivers will detect the most similar frequency change?" or something, so that the answer they expect you to put is not actually incorrect.