What Frequency Does a Worker Hear at Rest?

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Homework Help Overview

The problem involves a 2000Hz siren and a worker, both at rest with respect to the ground, while wind is blowing toward the worker at 12m/s. The discussion centers on determining the frequency the worker hears under these conditions.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the effects of wind on sound frequency, questioning the movement of the worker and the siren relative to the medium. There are discussions about the correct application of the Doppler effect formula and the implications of the wind speed on sound propagation.

Discussion Status

The discussion is ongoing, with participants examining different frames of reference and the implications of wind on the perceived frequency. Some guidance has been offered regarding shifting perspectives to understand the problem better, but no consensus has been reached on the correct interpretation of the situation.

Contextual Notes

There is some confusion regarding the movement of the worker and the siren in relation to the wind, as well as the implications of being stationary versus moving in the medium. The original poster's calculations are questioned, and assumptions about the setup are being examined.

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Homework Statement



2000Hz siren and worker are both at rest with respect to ground. What frequency does worker hear if the wind is blowing toward him from the siren at 12m/s?

Homework Equations



f'=f(v/v-vs)

The Attempt at a Solution



So since the worker is stationary, Vd in the numerator is 0. So the answer I got was:
2000*(343/(343-12)) = 2073Hz. Is this correct?
 
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The air is the medium carrying the sound waves. With a steady wind of 12m/s, both the siren and the worker are moving with respect to the medium.
 
gneill said:
The air is the medium carrying the sound waves. With a steady wind of 12m/s, both the siren and the worker are moving with respect to the medium.

not understanding how the worker is moving. If he is moving then in what direction? So I can determine + or -. I originally thought the worker was stationary which led vd to be 0 in the numerator. I see the source is moving toward the worker so the - sign is used.
 
Does the distance between worker and source change?
 
One way that you might look at the problem is to imagine that you shift your point of view to that of the medium itself. That is, change your frame of reference so that it is stationary with respect to the air. In that frame of reference you have a stationary medium but the source and receiver are moving. How are they moving you ask? Consult the attached figure.

As you can see, in such a frame of reference both the source and receiver are moving at the same speed and direction. The direction is opposite that of the wind direction in the "ground frame".

If you like, another way to approach the problem is to consider that the wind speed is simply added to the sound speed (for sound moving in the direction of the wind), leaving the source and receiver velocities alone (zero in this case).
 

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so, if the source and worker are stationary (zero) then the frequency heard would just be 2000Hz?
 
Is that what your calculations show? Then it must be true!
 

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