Doppler effect wavelengths

1. Apr 27, 2006

endeavor

"Is there a Doppler effect if a sound source and an object are moving at right angles?"

I assume this means that both are moving away from a single point...
I thought there would be a Doppler effect because both objects are moving and therefore the sound produced has an effective longer wavelength.

However, the answer in the back of my book is a simple "no". What am I doing wrong?

Last edited: Apr 27, 2006
2. Apr 27, 2006

Staff: Mentor

It means that the source is moving sideways instead of towards or away from the observer. The sound source must be moving towards or away from you to have a Doppler effect. (Not so relativistically: Look up the "transverse Doppler effect" for light.)

3. Apr 27, 2006

Staff: Mentor

I think the problem is not stated very well. Just because the dot product of the two velocity vectors is zero, doesn't mean that the time derivative of the difference between their two position vectors is zero (which would have to be true for there to be no Doppler shift).

Take the case of a person riding up an outdoor elevator as a train goes by on the ground directly below him. Of course he will hear a Doppler shift up as the train approaches the spot on the ground below him, and a Doppler shift down after the train passes. If the problem wanted to have the answer be "no", then it should have constrained the question to the instant when one of the objects passes through the axis of motion of the other object.

4. Apr 27, 2006

Homer Simpson

I agree with berkeman. In my mind, if two objects are closing in on one another or separating during a givin time period, then the doppler effect will be heard. If the two objects were moving at right angles such that the hypotenueuse of the triangle would stay a constant length (quarter quadrants of a circle??) then I think no.

5. Apr 27, 2006

Staff: Mentor

Right. I should have made that clearer in my response. (And I agree that the problem is poorly stated.) Only at one instant will the Doppler effect be truly zero. (Good catch! )

6. Apr 27, 2006

endeavor

So my answer could be correct?

I'm not sure I understand your explanations 100%, but I think I get it. I'm only taking an introductory physics course so I haven't learned anything other than the source/observer moving away/toward each other; and I didn't learn about using vectors with the Doppler effect either.

7. Apr 28, 2006

Staff: Mentor

Given your perfectly reasonable interpretation of the ambiguous statement "moving at right angles" as meaning, say, that the source is moving east while the observer is moving north, then a Doppler effect will most likely be observed. (As berkeman explained.) The key is: Is the distance between observer and source changing? If yes, then there's a Doppler effect; if no, no Doppler effect. (If the source is moving towards the observer, the observed frequency is higher; if it is moving away, it's lower.)

What they probably meant to say was something like: "Is a Doppler effect observed if the source moves (with respect to the observer) at a right angle with respect to the line between source and observer?" In that case the answer is no.

I'm curious, what's the exact statement of the question in your book?

8. Apr 28, 2006

endeavor

Well the exact statement just happens to be almost the same, and is still ambiguous.
Even part (a) is ambiguous. However, I know they must mean that both the source and the observer are moving in the same direction with the same velocity, because the answer is no. For part c, the frequency would be increasing.

9. Apr 28, 2006

Staff: Mentor

Actually, the term "velocity" often denotes the velocity vector (as opposed to the scalar term "speed"), so in that sense, (a) isn't ambiguous. (c) works too, and I think we all agree that (b) is ambiguous. Maybe you'll get extra credit for pointing out why (b) is ambiguous...?

10. Apr 28, 2006

endeavor

Oh yeah, I was thinking about speed. Yeah, I'll see if I can get some extra credit