GRE Doppler Effect Question

[PsychonautQQ]

Homework Statement

http://grephysics.net/ans/8677/12

I don't understand how it increases it's frequency by a factor of 10, I mean the total velocity goes from 1 to 1.9, therefore It seems like it should increase from 1kHz to 1.9kHz. Why is my 'common sense' wrong?

 

[Doc Al]

I don't understand how it increases it's frequency by a factor of 10, I mean the total velocity goes from 1 to 1.9, therefore It seems like it should increase from 1kHz to 1.9kHz. Why is my 'common sense' wrong?

What does the Doppler formula give you for the observed frequency when the source is moving? Not sure what you mean by "total velocity"--realize that the source is moving towards the listener.

(I misread the problem myself, the first time through.)

 

[PsychonautQQ]

frequency receiver = (velocity sound + velocity sender) * frequency sender
with velocity of sound = c and velocity of sender = .9c, It seems the frequency received is 1.9 the original frequency. No?

 

[Doc Al]

frequency receiver = (velocity sound + velocity sender) * frequency sender
with velocity of sound = c and velocity of sender = .9c, It seems the frequency received is 1.9 the original frequency. No?

No.

The Doppler formula for an approaching source is:
$f' = \frac{v}{v - v_s} f$
where $v_s$ is the speed of the source.

See: Doppler Effect

 

[PsychonautQQ]

Okay so the correct Doppler effect the source is in the denominator, I don't understand qualitatively why it matters though. Whether it's the receiver or sender that's movie, the relative velocity between them is going to be the same?

 

[Doc Al]

Okay so the correct Doppler effect the source is in the denominator, I don't understand qualitatively why it matters though. Whether it's the receiver or sender that's movie, the relative velocity between them is going to be the same?

Note that relative velocity (of source and observer) doesn't enter into the Doppler formula (at least for sound). The speeds are relative to the air. And that a moving source differs from a moving observer. (Compare the two cases, even for the same speed.)

To understand how this is, you'll need to review the details of the derivation of the formula.