Doppler shift with 2 trombones

[Gauss M.D.]

Homework Statement

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?

Homework Equations

f = f₀/(1-v_s/v)

Speed of sound = 340m/s

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?

 

[STEMucator]

Homework Statement

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?

Homework Equations

f = f₀/(1-v_s/v)

Speed of sound = 340m/s

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?

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?

 

[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?

 

[STEMucator]

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?

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.

Paul is approaching her at speed $v$, blowing the same type of trombone.

 

[Gauss M.D.]

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

 

[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 v_s 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.

 

[STEMucator]

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

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.

 

[haruspex]

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

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.

 

[STEMucator]

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.

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.