# Effect of wind shear on noise propagation

1. Jan 26, 2013

### CWatters

Can anyone recommend a source of information that quantifies how wind shear effects the propagation of sound/noise?

I know the basics in that wind shear either bends sound waves upwards or downwards but I'm looking for something that helps calculate the effect.

2. Jan 26, 2013

### sophiecentaur

The forward or rearward tilt angle of the sound wave front due to windshear will, I think be due the difference in speed of the sound at a height above ground.
I started thinking about this but came to an impasse. I don't know whether you have been here already but these are my thoughts:
The speed of the sound over the ground is c + v, where c is the speed of sound and v is the speed the air is travelling. So, if at height h, the air speed is Δv greater than the the speed on the ground, the wave front at h will be Δv faster. I thought that it should be possible to draw a triangle and work out the angle but, of course, in this simple model, the slope would depend upon time since the sound was launched (the dimensions are wrong unless you use tΔv). The sound in the higher air will, in fact, gradually overtake the sound on the ground. In fact, of course, sound would normally originate on the ground and the path of the sound energy launched at an upward angle to the ground would follow a curved path up and over the ground wave. The simple notion of 'wave tilt' really isn't enough to solve the problem. What you really need to be doing is to equate the propagation time along the curved aerial path to the time of the slower ground wave. At some distance, these will be equal and you will get a focussing effect. At this point I decided it was too hard for a Saturday evening.
I found a lot of rather useless links concerning the effect that the wind had on the progress of Civil war battles due to sound propagation and there was a lot of arm waving on the subject but I found precious little about the actual mechanics. I did find this link, which may be a start for you. At least it manages to have some equations, diagrams and references.

3. Jan 26, 2013

### Bobbywhy

Yes, Please see the following two Wiki pages for a few introductory remarks. To get intricate details of the mechanism, please see the three references shown.

"Wind shear can have a pronounced effect upon sound propagation in the lower atmosphere, where waves can be "bent" by refraction phenomenon. The audibility of sounds from distant sources, such as thunder or gunshots, is very dependent on the amount of shear."
http://en.wikipedia.org/wiki/Wind_shear

"Effects due to wind shear
The speed of sound varies with temperature. Since temperature and sound velocity normally decrease with increasing altitude, sound is refracted upward, away from listeners on the ground, creating an acoustic shadow at some distance from the source.[2] Wind shear of 4 m•s−1•km−1 can produce refraction equal to a typical temperature lapse rate of 7.5 °C/km.[5] Higher values of wind gradient will refract sound downward toward the surface in the downwind direction,[6] eliminating the acoustic shadow on the downwind side. This will increase the audibility of sounds downwind. This downwind refraction effect occurs because there is a wind gradient; the sound is not being carried along by the wind.[7]

5. Uman, Martin (1984). Lightning. New York: Dover Publications. ISBN 0-486-64575-4.

6. Volland, Hans (1995). Handbook of Atmospheric Electrodynamics. Boca Raton: CRC Press. p. 22. ISBN 0-8493-8647-0.

7. Singal, S. (2005). Noise Pollution and Control Strategy. Alpha Science International, Ltd. p. 7. ISBN 1-84265-237-0. "It may be seen that refraction effects occur only because there is a wind gradient and it is not due to the result of sound being convected along by the wind."
http://en.wikipedia.org/wiki/Speed_of_sound

Note: These data are typically used by environmental engineers while assessing sound propagation from noise sources that may pollute habitable spaces.

Cheers,
Bobbywhy

4. Jan 27, 2013

### CWatters

Thanks for that. I can see I'm going to have to take a trip to a good book shop.