doppler effect when source is approaching at constant speed

[AntonFreeman]

A roller skater carrying a portable stereo skates at constant speed past an observer at rest. which of the following accurately represents how the frequency perceived by observer with time?

I chose a graph that looks like upside down parabola showing increasing frequency and eventually decreasing frequency. however, solution says that if the speed of the source of sound does not change then frequency observed should not change either. observer would hear constant higher frequency when skater is approaching and constant lower frequency once skater passes the observer. could someone explain this? i thought that frequency increases as source of the sound approaches did not think that there has to be change in speed.

---

Members don't see this ad.

 

[V5RED]

Write out the doppler effect equation. Notice that the frequency shift observed depends only on the relative speed of the source and the listener, not their distance apart.

 

[Jengreef]

I'd like someone to clarify this as well. If frequency only shifts when speed of sound changes, then it seems to me that the apparent frequency would never shift to the observer unless the observer is in a different medium from the source, which is the only instance where you see speed of sound changing.

My answer agrees with the original poster. Observed frequency should increase as source approaches the observer at some velocity and decrease as the source moves away from the observer.

If it's not the speed of sound, but the speed of the observer and/or source we're discussing, velocity should still be constant in order for doppler equation to work doesn't it? If velocity changes as it approaches the observer, we aren't working with velocity, we're working with acceleration, and this element truly is absent in the doppler equation.

Am I misunderstanding something here?

 

[MangoPlant]

I agree with the OP. The observer will in fact observe a changing frequency; it will be higher as the skater is moving toward the observer and lower as the skater is moving away. This is the observed frequency, not to be confused with the emitted frequency.

If the question were asking about emitted frequency, the solution would be right. The emitted frequency can only be changed at the source of emission so it would stay the same, but the question clearly says "the frequency perceived by observer", which would be observed frequency. Thus I think the solution may be wrong?

 

[V5RED]

I really wish I could give a good explanation for why it is wrong to think that the frequency will change as the objects approach each other at a constant speed as opposed to having a set shift that does not change as they approach, but sadly my physics class skipped the doppler effect.

I will say that if you answer questions as if the doppler shift changes based on how close the objects are as opposed to their relative speeds(ie what OP said and got wrong on his practice material), you will absolutely get the question wrong on the MCAT.

 

[Jengreef]

I really wish I could give a good explanation for why it is wrong to think that the frequency will change as the objects approach each other at a constant speed as opposed to having a set shift that does not change as they approach, but sadly my physics class skipped the doppler effect.

I will say that if you answer questions as if the doppler shift changes based on how close the objects are as opposed to their relative speeds(ie what OP said and got wrong on his practice material), you will absolutely get the question wrong on the MCAT.

V5RED, the "correct" solution OP provided stated nothing about the relative distances between the two. It states that because speed is kept constant, the observed frequency didn't change, which makes absolutely no sense. The Doppler equation doesn't account for acceleration of the two bodies, it accounts for velocity of the two, which is assumed to be constant and unchanging.

Since you haven't covered Doppler Shift in your physics class, I'm assuming you're pulling your answers from some other credible source. Can you provide for us where this is coming from?

 

[V5RED]

V5RED, the "correct" solution OP provided stated nothing about the relative distances between the two. It states that because speed is kept constant, the observed frequency didn't change, which makes absolutely no sense. The Doppler equation doesn't account for acceleration of the two bodies, it accounts for velocity of the two, which is assumed to be constant and unchanging.

Since you haven't covered Doppler Shift in your physics class, I'm assuming you're pulling your answers from some other credible source. Can you provide for us where this is coming from?

The observed SHIFTED frequency remains constant. In other words, the frequency is shifted due to the relative speeds, but this shift does not change as they approach each other.

OP's answer says that this shift becomes larger as they approach each other(ie the parabolic graph) which would mean that their relative separation was playing a role.

My answers are based on TBR and EK physics as well as the application of the doppler equation which tells you that the shift is changed by a relative velocity between the sender and receiver, but this shift remains constant unless relative velocity changes. In other words if 2 objects approach each other and one is sending a 400Hz wave and it shifts to an apparent 450Hz wave, it remains a 450Hz wave until they either change velocities or they pass each other.

 

[MangoPlant]

The observed SHIFTED frequency remains constant. In other words, the frequency is shifted due to the relative speeds, but this shift does not change as they approach each other.

OP's answer says that this shift becomes larger as they approach each other(ie the parabolic graph) which would mean that their relative separation was playing a role.

My answers are based on TBR and EK physics as well as the application of the doppler equation which tells you that the shift is changed by a relative velocity between the sender and receiver, but this shift remains constant unless relative velocity changes. In other words if 2 objects approach each other and one is sending a 400Hz wave and it shifts to an apparent 450Hz wave, it remains a 450Hz wave until they either change velocities or they pass each other.

This is correct. The graph would look like a horizontal line until the point at which the skater passed the observer at which it would dip down and then proceed horizontally once again (lower than the original horizontal line). If the velocity of the skater was changing, then the graph would be like that of y=1/x

 

[sciencebooks]

The observed SHIFTED frequency remains constant. In other words, the frequency is shifted due to the relative speeds, but this shift does not change as they approach each other.

OP's answer says that this shift becomes larger as they approach each other(ie the parabolic graph) which would mean that their relative separation was playing a role.

My answers are based on TBR and EK physics as well as the application of the doppler equation which tells you that the shift is changed by a relative velocity between the sender and receiver, but this shift remains constant unless relative velocity changes. In other words if 2 objects approach each other and one is sending a 400Hz wave and it shifts to an apparent 450Hz wave, it remains a 450Hz wave until they either change velocities or they pass each other.

This makes sense, but up until the observer, that the magnitude of shift would be the same to/away. But the shift would change once the source passed the object since perceived frequency would be higher while approaching and lower while skating away, right?

 

[V5RED]

This makes sense, but up until the observer, that the magnitude of shift would be the same to/away. But the shift would change once the source passed the object since perceived frequency would be higher while approaching and lower while skating away, right?

Correct.

Also, I am pretty sure there would be no shift at the instant where they are passing each other since their relative velocity would be zero.

 

[MangoPlant]

Correct.

Also, I am pretty sure there would be no shift at the instant where they are passing each other since their relative velocity would be zero.

I'm not so sure about this. Their relative velocity is not 0 when they are passing each other, their relative distance may be 0 but I don't think distance would result in no shift. I say the shift would either be a near-vertical line or a parabolic curve.

 

[V5RED]

I'm not so sure about this. Their relative velocity is not 0 when they are passing each other, their relative distance may be 0 but I don't think distance would result in no shift. I say the shift would either be a near-vertical line or a parabolic curve.

Their relative distance would only be zero if they occupied the same space.

You are right that their relative velocity is not zero, but in the direction that matters for a doppler shift (ie from object one directly to object two) their relative velocity is zero. Yes, their velocities point in opposite directions, but the velocity in the direction directly from object A to object B is zero when they are side by side.

 

[MangoPlant]

Their relative distance would only be zero if they occupied the same space.

You are right that their relative velocity is not zero, but in the direction that matters for a doppler shift (ie from object one directly to object two) their relative velocity is zero. Yes, their velocities point in opposite directions, but the velocity in the direction directly from object A to object B is zero when they are side by side.

Oh, I'm sorry I misread what you were originally saying. If you were saying that the emitted frequency = observed frequency at the point the two objects pass each other, I agree with you. Sorry for the confusion! 😳

 

[V5RED]

Oh, I'm sorry I misread what you were originally saying. If you were saying that the emitted frequency = observed frequency at the point the two objects pass each other, I agree with you. Sorry for the confusion! 😳

That is what I was saying. Sorry for my confusing wording.

 

[sciencebooks]

Correct.

Also, I am pretty sure there would be no shift at the instant where they are passing each other since their relative velocity would be zero.

👍 Sounds good.

So there'd be one shift, then no shift, then another shift. How would that even look if they tried to graph that?

 

[MangoPlant]

👍 Sounds good.

So there'd be one shift, then no shift, then another shift. How would that even look if they tried to graph that?

Like I said in an earlier post, straight line then parabolic section and then more straight line. If you know what an integral looks like: straight line, a reverse integral symbol, and then more straight line.

Kind of like this:http://amateurgeophysics.files.wordpress.com/2008/11/fobserved.gif

 

[sciencebooks]

Like I said in an earlier post, straight line then parabolic section and then more straight line. If you know what an integral looks like: straight line, a reverse integral symbol, and then more straight line.

Kind of like this:http://amateurgeophysics.files.wordpress.com/2008/11/fobserved.gif

I get the straight lines, but why parabolic in the middle? I thought it'd go down to zero.

 

[Jengreef]

Well, observed frequency wouldn't go down to zero. V5RED explained it well I think (btw, thank you for the clarification, and forgive me for doubting you).

While intensity decreases until zero, observed frequency would in fact be constant during the approaching region, change the very instant that the source and observer are neither approaching towards nor moving away from each other (I'm guessing this is the parabolic region), then change once more as source moves away from observer, but this observed frequency itself would be static as soon as the source is moving away from the observer, and would actually not decrease any more following that (or decrease only a negligible amount).

That said, I'd also like additional clarfication on the parabolic region. Or rather, maybe you could define parabolic because I keep wanting to think of a U shaped curve where there's a decrease followed by an increase or vice versa. There's a lot I still don't know about graph functions, so there's probably something I don't understand about parabolas here.

By the way, Craig Bohren agrees with you all. 😉

 

[V5RED]

I get the straight lines, but why parabolic in the middle? I thought it'd go down to zero.

This is a guess since I only know doppler effect well enough to get through MCAT level problems(everything I posted so far in this thread is MCAT level doppler effect stuff because that is all I know), but I would guess that since the objects don't literally pass through each other, the doppler effect only fits the ideal mold of the doppler equation when they are not very close to each other.

The doppler equation assumes that the objects are moving directly toward or away from each other, but things that pass each other obviously are not moving that way or they would collide and stay stuck together. I would then guess that once they get close enough together, this difference in how fast they move in the direction their velocity actually points compared to how fast they approach each other becomes larger and larger which would lead to the curve in the middle of the graph.

I would guess that a problem that asked about the doppler effect in that parabolic region would require calculus to solve and thus not be applicable to the MCAT.

Of course I could be totally wrong. I am just guessing based on what makes the most sense to me because my teacher skipped this stuff.

 

[Godric]

just curious, where is this problem from?

 

[NuttyEngDude]

just curious, where is this problem from?

i've seen this in kaplan material.