What Frequency Does a Worker Hear at Rest?

[ee1215]

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?

 

[gneill]

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.

 

[ee1215]

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.

 

[Borek]

Does the distance between worker and source change?

 

[gneill]

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).

 

[ee1215]

so, if the source and worker are stationary (zero) then the frequency heard would just be 2000Hz?

 

[gneill]

Is that what your calculations show? Then it must be true!