Confusion regarding the speed of sound in wind

[CooperPears]

One of my students asked me the seemingly innocuous question of "how does wind affect the speed of sound?". My immediate thought was that the velocity of the wave would be the vector sum of the velocity of the wind and the velocity of sound waves in still air. However, upon further reflection I came to the conclusion that the wave should have the same velocity regardless. My reasoning is this: the speed at which the disturbance propagates THROUGH the medium should not affected by the velocity of the medium itself. Imagine that the air is a lattice of tiny particles connected by springs. Whether or not the lattice is moving as a whole would have no effect on the time it would take for a disturbance to travel between two arbitrary points. In short the dynamics of how the disturbance gets transmitted through the medium have not been altered by the introduction of a medium velocity. Thus the way I see it is that unless wind appreciably changes the bulk modulus of air, then the velocity should remain the same.

I have read some forum responses online that indicate my reasoning is flawed, and that my first impression of the system was indeed correct and that the velocity is just a superposition. If so, can you help me identify the flaw in this logic?

Thank You

 

[whit3r0se-]

In fluid dynamics we conventionally model the medium of air to be like static particles, the scenario you have described here is the opposite. An analogy that might help you understand is a static pond, imagine swimming through there and now compare that to swimming through a sea full of currents. Whilst swimming through a sea full of currents it's quite obvious that your velocity can be modeled by the vector sum of the current and yourself. Your chain of reasoning is also dependent on the frame of reference of the observer, so can you please clarify?

 

[CooperPears]

Your thinking would apply if sound was transmitted by air particles moving from source to observer but that is not true.

 

[whit3r0se-]

Could you clarify the frame of reference?

 

[CooperPears]

the frame of reference is stationary ground i.e. the one in which the wind velocity is measured

 

[whit3r0se-]

If your frame of reference is the ground then the speed of sound from your perspective will be the speed of the medium + speed of sound through the wind

 

[boneh3ad]

Well the flaw in the logic is really that air (or any gas) is not a lattice of molecules interconnected by springs. That more accurately describes a solid. Even then it would still be dependent on the motion of the lattice when observed from a stationary frame.

For a given set of of conditions, the speed of sound is constant with respect to the medium of travel. If a stationary observer is standing in the wind, he or she will observe sound waves moving at a velocity that is the vector sum of the sound speed at those conditions and the wind speed.

 

[CooperPears]

You are of course correct in that it is not prudent to model a gas as a lattice of particles connected by springs. I was not suggesting we use that model, but since I am referring to the stiffness (bulk modulus) of air, I thought that would get my point across but clearly it didn't. Apologies.

Like you said, the speed of sound w.r.t to the medium is constant for a set of conditions. What I am saying is that since wind is the net translation of air particles, and sound is not transmitted by the net translation of air particles, it shouldn't affect the time it takes the sound to travel between two points. Assuming of course that wind and still air have the same bulk modulus.

 

[CWatters]

My immediate thought was that the velocity of the wave would be the vector sum of the velocity of the wind and the velocity of sound waves in still air. However, upon further reflection I came to the conclusion that the wave should have the same velocity regardless. My reasoning is this: the speed at which the disturbance propagates THROUGH the medium should not affected by the velocity of the medium itself.

Your last line seems to be arguing in favour of your "immediate thought" rather than your "further reflection".

 

[russ_watters]

Your last line seems to be arguing in favour of your "immediate thought" rather than your "further reflection".

Agreed. This odd argument with yourself seems like it should come to one conclusion, not two different ones.

 

[The Bill]

Imagine that the air is a lattice of tiny particles connected by springs. Whether or not the lattice is moving as a whole would have no effect on the time it would take for a disturbance to travel between two arbitrary points. In short the dynamics of how the disturbance gets transmitted through the medium have not been altered by the introduction of a medium velocity.

You're assuming that the source and destination points stay in the same positions relative to the medium in the case with a medium velocity as in the case with no medium velocity. They don't.

Imagine a speaker which emits a very short chirp, which is then detected by a microphone 340 meters down a wind tunnel. Assume that the conditions in the wind tunnel are adjusted so that the speed of sound is 340 meters per second.

First, we do the experiment with no wind, and we measure the chirp at the microphone 1.000s after the speaker sounded.

Next, we set the wind tunnel to provide a 10m/s wind from the speaker to the microphone. After 34/35 of one second has passed, the position in the medium where the sound originated is 9.714m away from the speaker, and the sound wave has traveled 330.286m within the medium, reaching the microphone.

Basically, a moving medium invalidates your assumption that the source and destination stay the same distance apart within the medium.

 

[A.T.]

sound is not transmitted by the net translation of air particles

You seem to be misinterpreting this part. Uniform bulk translation of air particles doesn't constitute sound, but it does effect the propagation speed of sound created otherwise.