Simple doppler effect question

[AOT11]

I'm usually really good at physics, but this simple AAMC question has me tripped up. It's from AAMC 4 - they presented the doppler equation in ways I have never seen.

Delta f over f = -v/c
and
Delta lambda/lambda = v/c

What are these equations saying? I've never seen them in this form! Any help would be appreciated!

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[EnginrTheFuture]

I'm usually really good at physics, but this simple AAMC question has me tripped up. It's from AAMC 4 - they presented the doppler equation in ways I have never seen.

Delta f over f = -v/c
and
Delta lambda/lambda = v/c

What are these equations saying? I've never seen them in this form! Any help would be appreciated!

I would attempt to explain this but since wiki already did it fairly well I thought I would point you there:

http://en.wikipedia.org/wiki/Doppler_effect

Under "general" it has that form of the equation, when it is valid and how it is derived. If you still do not get what it is saying, post up and I'll give it a whirl!

best of luck

 

[AOT11]

I would attempt to explain this but since wiki already did it fairly well I thought I would point you there:

http://en.wikipedia.org/wiki/Doppler_effect

Under "general" it has that form of the equation, when it is valid and how it is derived. If you still do not get what it is saying, post up and I'll give it a whirl!

best of luck

I read through it, but it still doesn't make any sense 🙁

 

[EnginrTheFuture]

Let me first talk about :

(Delta f)/f = -v/c -----> (Delta f) = (-v/c) x f

-----> Change in frequency = a fraction of original frequency

note that v is actually (V_source - V_receiver) a.k.a. how fast the source is traveling away or towards the receiver. Positive means it is going away from the receiver, negative means it is traveling towards the receiver.

This formula is valid only in the limit that the wave speed is much much greater than the difference in velocity between the source and receiver. This is definitely the case with electromagnetic waves because very few things are emitting waves whilst traveling at you near the speed of light 😀. Sound waves which travel much slower than light (340 m/s as compared to 3x10^8 m/s) can be emitted by something traveling almost that fast (a jet for instance) so this different relationship is set up to describe light for convenience. It can also be used to describe sound emitted by a source traveling really slowly.

What it is saying is that the change in frequency is directly proportional to the velocity difference between emitter and listener divided by the speed the wave travels. For simplicity, if the receiver is standing still, the frequency change is (f_original )(-V_source/speed of wave) where positive velocity is defined as "away". Thus if a source is traveling towards you, the V_source is negative and the frequency change is a positive gain (higher frequency), as you would expect. The faster the source travels towards you, the greater the v/c and thus the larger the increase. The same "idea" (cause and effect) applies to the formula you are used to and this one, this one is just a special one you can use for light or slow moving sources. This relationship is not true when you approach the other limit (when the wave travels about the same speed as the source is approaching the receiver).

As the velocity difference between emitter and detector gets very large, the change in frequency becomes a greater fraction of the original frequency. This makes sense, right?

This is just another relationship like the "usual" doppler equation but for the special case of Speed of wave >> (V_source - V_receiver)

 

[AOT11]

Let me first talk about :

(Delta f)/f = -v/c -----> (Delta f) = (-v/c) x f

-----> Change in frequency = a fraction of original frequency

note that v is actually (V_source - V_receiver) a.k.a. how fast the source is traveling away or towards the receiver. Positive means it is going away from the receiver, negative means it is traveling towards the receiver.

This formula is valid only in the limit that the wave speed is much much greater than the difference in velocity between the source and receiver. This is definitely the case with electromagnetic waves because very few things are emitting waves whilst traveling at you near the speed of light 😀. Sound waves which travel much slower than light (340 m/s as compared to 3x10^8 m/s) can be emitted by something traveling almost that fast (a jet for instance) so this different relationship is set up to describe light for convenience. It can also be used to describe sound emitted by a source traveling really slowly.

What it is saying is that the change in frequency is directly proportional to the velocity difference between emitter and listener divided by the speed the wave travels. For simplicity, if the receiver is standing still, the frequency change is (f_original )(-V_source/speed of wave) where positive velocity is defined as "away". Thus if a source is traveling towards you, the V_source is negative and the frequency change is a positive gain (higher frequency), as you would expect. The faster the source travels towards you, the greater the v/c and thus the larger the increase. The same "idea" (cause and effect) applies to the formula you are used to and this one, this one is just a special one you can use for light or slow moving sources. This relationship is not true when you approach the other limit (when the wave travels about the same speed as the source is approaching the receiver).

As the velocity difference between emitter and detector gets very large, the change in frequency becomes a greater fraction of the original frequency. This makes sense, right?

This is just another relationship like the "usual" doppler equation but for the special case of Speed of wave >> (V_source - V_receiver)

Your answer was PERFECT! thank you so much!

Although to be honest, I do think they made a simple concept (the doppler effect) seem much harder than it really is. I have never encountered that version of the equation, and I was an aerospace engineer 😡