How Does Wind Affect the Doppler Shift of Sound?

[e(ho0n3]

Homework Statement

A factory whistle emits sound of frequency f. On a day when the wind velocity is w from the north, what frequency will observers hear who are located, at rest, (a) due north, (b) due south, (c) due east, and (d) due west, of the whistle? What frequency is heard by a cyclist heading (e) north or (f) west, toward the whistle at a speed u?

Homework Equations

Frequency heard by stationary observer of a sound source

(1) moving toward the observer: f/(1 - v_s/v);
(2) moving away from the observer: f/(1 + v_s/v).

Frequency heard by a moving observer of a stationary sound source when

(3) the observer is moving toward the source: f(1 + v_o/v);
(4) the observer is moving away from the source: f(1 + v_o/v).

f is the frequency of the sound source, v is the velocity of sound in air, v_o is the velocity of the observer and v_s is the velocity of the sound source.

The Attempt at a Solution

This problem is a bit tricky for me because it discusses a new concept: waves on a moving medium, viz. sound waves in the wind. I thought of a simpler situation: a transverse wave on a moving string. In this situation, if the wave moves in the same direction as the string, an observer will see a faster moving wave than one in which the string is not moving right?

The question is: Do I consider the wind as a moving sound source then?

 

[denverdoc]

Not sure. From intuition I would, but I would clearly state as an assumption that v plus c add vectorially.

 

[e(ho0n3]

I checked the answer in the book. It seems that they ignore the velocity of the wind because the answers to (a) - (d) are all f. I wonder if this was a trick question.

 

[denverdoc]

Yea, the advection for wind + c is fairly minimal, dissipation is not.

 

[e(ho0n3]

What do you mean by "advection for wind + c"? I don't get it. If I'm ignoring the wind, would the answers to (e) and (f) be the same?

 

[denverdoc]

No, the first four parts assume (or not)a vector addition of wind and c, whereas e,f are based on the motion of the observor.

 

[e(ho0n3]

You keep referring to c. What is c? Also, the cyclist is moving toward the whistle so it doesn't matter if he is moving towards it from the south or from the west.

 

[denverdoc]

c is the speed of sound. a-d involve at rest bodies, while e,f are at motion relative to the whistle.

 

[stefjourdan]

Please read also our article : "The Doppler effect's contribution in the propagation of sound on a windy day" http://knol.google.com/k/athena-jourdan/the-doppler-effect-s-contribution-in/airq7uy58x6t/40#

cheers

S. J.