Sky Diving Washington
The Doppler effect's contribution in the propagation of sound on a windy day
Why can wind transmit the noise so effectively in the direction of the flow and mitigate it so much in the opposite direction ?In the preferential travel of sound in the direction of the wind and its poor travel in the reverse direction we certainly have cumulative effects. This article shows that one of them is a double Doppler effect, or rather a double Dopplerization combined with a frequency dependent attenuation.
(physics, acoustics)
This original article was written in french for Knol in December 2008 and translated to english in january 2009, many thanks to BJ for his help.
Many people are surprised that the wind (wind speeds are on the order of 10 m/sec, often much less) may change the range of sound that propagates much faster (the speed of sound is on the order of 350 m /sec). Some people have not experimented this personally and comically try to check on the internet the truth of this experiment, which is well-known to people living in the countryside.
The Doppler effect
The Doppler effect is usually presented as a phenomenon linked to a change of distance between a source and a receiver.
Appreciate this very surrealistic drawing from http://www.fygo.dk/files/ukursus/Ultrasound%20Doppler.pdf
(The smoke from the locomotive, which is inhaled by the musician, is not shown ...)
For example, the entry on the Doppler effect in Wikipedia (in french, 2008) states that:
"The Doppler effect or D. shift ...... is the change in frequency and wavelength of a wave for an observer moving relative to the source of the waves."
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| Page extracted from "waves_doppler.ppt", a presentation from the site, http://www.csulb.edu (California State University at Long Beach) through the link http://www.filestube.com/e345996af8ec0b9f03e9/go.html. the author seems to be Igor Glozman, a professor now at Higline Community College, Des Moines, WA, USA (?) |
In this page, the author tends to forget that the medium (the air) itself can move too [1] ... but it is already an improvement over 90% of presentations which always talk about the ambulance that passes by us, forgetting the stopped ambulance, with the siren blaring, at the side of the road when we are passing by (You could say that ambulances do not turn on the siren when stopped, but then I would answer: Fool ! This is an example in which there is no ambulance in fact! It was given here to understand the Doppler effect...).
So the present article has the bonus to show that the medium can be still relative to the source or still relative to the listener. If the Doppler shift on the listener is the similar, physically the wave train is distorted only if the emitter is moving relative to the medium (the second figure). Otherwise, a deformation of the wave train cannot be represented (the third figure).
In the previous schemes, the Dopplerization occurs only once, at the sender's place or at the receiver's, as appropriate, in fact at the place where there is a difference in speed. But what do we call "Dopplerization"? We must distinguish it from the effect usually described - the frequency change observed by a person or an appliance. We call Dopplerization the "distortion" of the wave field (effective, real, and active and occurring when there is a difference in speed between the transmitter and the air) or virtual and passive (speed
differential between the receiver and air). In both cases, this Dopplerization changes a concentric field to a non-concentric field or conversely, or even between two non-concentric fields:
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| Real Dopplerization: The wave field is distorted. CAUTION: This pattern, which usually represents a moving sound source in fixed air (but which may also represent a stationary source in moving air) does not mean that the wave will propagate slower to the right (the wave propagrates at the same speed in all directions). It does not either represent the range of the waves. This diagram only shows that the wavelengths are packed on one side and stretched on the other. Please do not look at this figure any longer, I mean it! I now count to three and you will wake up, pick up your clothes, and return to your seat, thank you... |
In short, the traditional ways of presenting the Doppler effect describes the result of single dopplerisation and not its operation (with its two aspects), and tends to overlook the possiblity that the phenomenon could be involved in situations where the distance between transmitter and receiver does not change, a possibility that we will now develop.
To be fair, this matter happened to be briefly discussed in a forum that we found by chance during the writing of this article [2]. Of course, I thank you for reporting any article that could address the issue (a forum in english was later discovered as well [3])
The propagation of sound and atmospheric refraction
Articles studying the propagation of sound (often in a noise control perspective) [4] between a stationary source and a stationary receiver evidently include wind as a factor which could change the propagation of the sound. They describe the refraction of sound waves within a wind gradient (The temperature gradient is also sometimes included) as the main cause of enhanced propagation in the direction of the wind and the poor propagation against the wind. A demonstration:
The wind is weaker near the ground than in altitude because of friction. This induces a gradient of intensity in the wind between the ground and a certain altitude, which is well known to balloonists and aviators (There is also a gradient of wind direction, because fast-moving air masses are subject to greater Coriolis force. Thus a slow-moving particle of air is deflected less by the Coriolis effect, but this is irrelevant to us.)
In the gradient of intensity sounds are moving at different speeds in different directions wich produces refraction:
In the direction of the wind, the speed of sound waves relative to the source increases with altitude as the wind speed increases. In the direction opposite to the wind, the speed of sound waves defined in the same way decreases with height.
Refraction bends the waves toward the direction of a lower propagation speed so:
The sound energy is deflected toward the ground downstream of the wind, while it is deflected into the sky upstream of the wind.
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| http://www.pa.op.dlr.de/acoustics/ |
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| In those drawings, the shown refraction can be caused by the wind gradient or by the temperature gradient, which we do not discuss. |
It is clear that the refraction explain part of the difference in transmission in the propagation of sound with the wind and against the wind that we observe. For example, if you live near a road, even a slight wind may bring you the noise of the road or may hide the noise from you, depending on the direction in which it blows.
This effect also explains why the sound "carried" by the wind is able to overcome some obstacles by "jumping over", a phenomenon early discovered by those who built the first anti-noise walls!
However, this theory has a weakness: the propagation of sound is also dependent on the nature of the "ground." This can be demonstrated at a lake with no wind and no waves. There, you can hear the noises coming from the other side, whereas if it were a field, you would certainly hear nothing ! In a normal terrain in the direction of the wind, the sound waves deflected towards the ground would be muffled and absorbed, and it is not clear how these deflected waves could recover to keep on going in the good direction, i.e., the horizontal direction. In fact, the refraction theory better explains the poorer sound propagation against the wind than the good propagation in the direction of the wind.
A complementary theory: the double dopplerisation
In our model the wind gradient is not necessary. The wind could be homogeneous, but the presence of a wind gradient does not interfere with its operation. At the time of the emission of the sound, the sound frequencies are dopplerized by the difference in speed between the stationary emitter and the medium of propagation, air (Physically, there is no difference between this case and a mobile source in still air. The deformation of the wave train is the same).
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