Hearing the Train Whistle Frequency: Calculating fs

[chem31sa6]

Homework Statement

You are standing on a train station platform as a train goes by close to you. As the train approaches, you hear the whistle sound at a frequency of f1 = 92 Hz. As the train recedes, you hear the whistle sound at a frequency of f2 = 79 Hz. Take the speed of sound in air to be v = 340 m/s.

Find the numeric value, in hertz, for the frequency of the train whistle fs that you would hear if the train were not moving.

Homework Equations

f obs = f s (v +- vobs / v +- vs)

The Attempt at a Solution

I tried to find fs by fs = f obs / (v +- vobs / v +- vs), but since nobody is moving I just get 1 in parenthesis, and don't know what to set f obs to. The correct answer is 85 Hz, I just have no clue how to get to that point.

 

[kuruman]

... but since nobody is moving ...

Isn't the train moving?

 

[chem31sa6]

Isn't the train moving?

Well it says to find the numeric value, in hertz, for the frequency of the train whistle fs that you would hear if the train were not moving.

 

[kuruman]

You quoted the relevant equation
$$f_{obs}=f\frac{v \pm v_{obs}}{v \pm v_{s}}$$
Can you identify what these symbols stand for? For example,
v = speed of sound, here 340 m/s.
What about $f$, $f_{obs}$, $v_{obs}$ and $v_s$? Can you say with words what they stand for and, if known, what their values are?

 

[chem31sa6]

You quoted the relevant equation
$$f_{obs}=f\frac{v \pm v_{obs}}{v \pm v_{s}}$$
Can you identify what these symbols stand for? For example,
v = speed of sound, here 340 m/s.
What about $f$, $f_{obs}$, $v_{obs}$ and $v_s$? Can you say with words what they stand for and, if known, what their values are?

f is the frequency produced from the source.
fobs is the frequency heard by the observer.
Vobs is the velocity of the observer (standing still so it has to be 0).
Vs is the velocity of the source, which in this part of the problem is the train which we are told stopped moving.

The only thing we have are the frequencies heard by the observer (92 and 79) along with the velocity of sound 340 m/s

 

[haruspex]

Vs is the velocity of the source, which in this part of the problem is the train which we are told stopped moving.

The only thing we have are the frequencies heard by the observer (92 and 79) along with the velocity of sound 340 m/s

But those data about the two frequencies heard apply to the case where the train is moving.

 

[kuruman]

f is the frequency produced from the source.

Indeed, and that is what the problem is asking you to find. What do you think given frequencies f1 = 92 Hz and f2 = 79 Hz are? Where do they come from and under what circumstances? If the train is not moving, the Doppler formula gives $f_{obs} = f$; that's nothing new. As @haruspex hinted, what does the formula look like when the train is moving?