Doppler shift with 2 trombones

1. Aug 5, 2013

Gauss M.D.

1. The problem statement, all variables and given/known data

Mary is blowing her trombone at 400hz.

Paul is approaching her at speed v, blowing the same type of trombone. These trombones has a maximum frequency of 500hz. What is the maximum speed Paul can approach Mary, and still cancel out her trombone noise?

2. Relevant equations

f = f0/(1-vs/v)

Speed of sound = 340m/s

3. The attempt at a solution

Max freq 500, so:

500 = 400/(1-v/340)

Solving for v, I get 68 m/s. The answer is 85 m/s. What's going on?

2. Aug 5, 2013

Zondrina

I don't think your equation is correct. Why are you saying the velocity v is equal to the speed of sound in the air?

Last edited: Aug 5, 2013
3. Aug 5, 2013

Gauss M.D.

The perceived frequency is equal to the real frequency divided by (1-v(speed of approaching source)/v(speed of sound)). Is that the wrong formula?

4. Aug 5, 2013

Zondrina

No that's not what I'm saying. This is indeed 100% correct after dividing through by v :

$f = \frac{f_0}{1 - \frac{v_s}{v}}$

I meant why are you using $v = 340 m/s$ in your calculation, it doesn't make any sense.

5. Aug 5, 2013

Gauss M.D.

Pauls speed divided by the speed of sound... What's wrong with dividing by 340?

6. Aug 5, 2013

haruspex

I agree with your calculations and answer of 68 m/s. 85 m/s is the answer if the question is how fast do you have to move away from a source of 500/s to hear it as 400/s.
Zondrina, you seem to be confused by the fact that the formula quoted uses vs for the speed of the source and v for the speed of sound, whereas in the question v stands for the speed of the source.

7. Aug 5, 2013

Zondrina

So Paul is coming at Mary at mach 1? I think you mean Paul comes at Mary with a speed of $v_s$ right :)?

As for your question though, I think you have worded it incorrectly, left information out or the answer is a typo.

If Paul is going away from Mary, then the answer of 85 m/s makes sense. $f$ is the apparent frequency and you said Mary plays the trombone at 400Hz. Hence $f = 400 Hz$ and so we can also say $f_0 = 500 Hz$. Then you get :

400 = 500/(1 - (v/340))
v = 85 m/s

EDIT : I'm not confused harup, I just believe he didn't put any effort into typing out the question properly.

Last edited: Aug 5, 2013
8. Aug 5, 2013

haruspex

Seems to me Gauss MD stated the question as given to him/her, and stated a formula in a reasonably standard form (though it is better to state what all the variables represent when quoting a formula). There should be no expectation that the two agree on allocation of symbols to entities.

9. Aug 5, 2013

Zondrina

Yes I agree I suppose, I'm just picky about notation IMO. I think information can get lost in translation through a problem if there isn't any consistency.